Exploiting internal resonance to improve flow energy harvesting from vortex-induced vibrations

Wake-galloping energy harvesting has been extensively developed to scavenge flow energy from vortex-induced oscillations. Hence, the wake-galloping harvester only has a natural frequency which leads to a very narrow bandwidth. Therefore, it does not operate well under the wide region of shedding frequencies in variable wind speed. To overcome the vital issue, this paper we explored a novel two-degree-of-freedom nonlinear flow energy harvester to collect flow energy induced by the wake of a bluff body. The nonlinear restoring force is realized by using a repulsive magnetic force between two cuboid-shaped permanent magnets, and the electromechanical coupling equations are presented. Based on the method of harmonic balance, the electromechanical governing equations are decoupled, and the first-order harmonic solutions are implemented. The modulation equations are established, and the amplitude–frequency figures of displacement and voltage are depicted with different detuning parameters. The superiority of the presented energy harvester is contrasted with the single-degree-of-freedom linear and nonlinear cases, and the results revealed that the two-degree-of-freedom nonlinear scheme can enhance the bandwidth of flow energy capture. The effect of physical parameters on the scavenged power is discussed. The accuracy and efficiency of the approximate analytical data are examined by numerical simulations.

A numerical simulation study was carried out to investigate the vortex-induced vibration (VIV) characteristics and energy harvesting performance (EHP) of flat plates with six types of concave and convex geometries at different Reynolds numbers (Re). The effects of concavity and convexity on vibration response, aerodynamic forces, and energy harvesting were analyzed, and the underlying mechanisms were elucidated from a fluid dynamics perspective. Results show that modifying the longitudinal edges of a baseline rectangular plate to concave or convex profiles significantly affects its VIV behavior. For convex plates, as the convexity increases, the VIV peak amplitude decreases, the wind velocity corresponding to this peak VIV amplitude decreases, and the vortex shedding frequency tends to increase. Both the vibration and energy harvesting efficiency of convex plates are significantly lower than those of the baseline plate. At a convex height-to-width ratio H * /D=0.35, the vibration displacement reaches its minimum, which is 99.83% lower than that of the baseline plate, demonstrating effective VIV suppression. Conversely, the concave plates exhibit higher vibration amplitudes and energy harvesting efficiency than the baseline plate. At H * /D =-0.35, the dimensionless peak vibration amplitude of the concave plate is 0.113, which is 107.57% higher than that of the baseline; correspondingly, the energy harvesting efficiency coefficient reaches its maximum. Moreover, studies under attack angles of 5° and 10° reveal that the concave plate with H * /D=-0.35 maintains enhanced energy harvesting performance across different inflow conditions, indicating good applicability in practice. Overall, these findings of this study offer valuable insights for improving energy harvesting efficiency through geometric modification.

Experimental study on characteristics of vortex-induced vibration of a twin-box girder and damping effects

A nonlinear hybrid piezoelectric (PE) and electromagnetic (EM) energy harvester is proposed, and its working model is established. Then the vibration response, output power, voltage and current of nonlinear hybrid energy harvester subjected to harmonic excitation are derived by the method of harmonic balance, and their normalized forms are obtained by the defined dimensionless parameters. Through numerical simulation and experimental test, the effects of nonlinear factor, load resistance, excitation frequency and the excitation acceleration on amplitude and electrical performances of hybrid energy harvester are studied, which shows that the numerical results are in agreement with that of experimental tests. Furthermore, it can be concluded that the bigger nonlinear factor, the lower resonant frequency; moreover, there is an optimal nonlinear factor that make the harvester output the maximum power. In addition, the output power of nonlinear hybrid energy harvester reaches the maximum at the optimal loads of PE and EM elements, which can be altered by the excitation acceleration. Meanwhile, the resonant frequency corresponding to the maximum power rises firstly and then falls with PE load enhancing, while it rises with EM load decreasing; furthermore, the frequency lowers with the acceleration increasing. Besides, the larger acceleration is, the bigger power output and the wider 3 dB bandwidth are. Compared with performances of linear hybrid energy harvester, the designed nonlinear energy harvester not only can reduce the resonant frequency and enlarger the bandwidth but also improve the output power.

A methodology is developed to analyze the vortex-induced vibration of moored or towed cable systems. The fluctuating forces are considered as sources of energy which generate waves propagating through the cable-body system with dissipation and scattering in the process. Because of its emphasis on energy flow, this method facilitates the incorporation of various vortex models into dynamic cable analysis. INTRODUCTION Cables exposed to current in deep-ocean moors or used for towing bodies or arrays for ocean survey are subject to transverse oscillations from vortex-induced forces. This phenomenon, called strumming, has been under investigation for many years because it affects the fatigue life of the structure and the noise of any attached sensors. Experiments conducted in water channels indicate that the vortex-induced vibration can be substantially reduced by introducing hydrodynamic disturbances to the flow near the structure. For example, mechanical devices, such as splitter vanes, trailing ribbons and fairings, have been used to disturb the formation of the vortex flow, while spiral wrappings have been used to disturb their spanwise coherence. Other investigations have been made concerning the nature of the vortex flow and to model the vortex-induced cable vibrations. Wind tunnel and water channel experiments were carried out to measure the characteristics of vortex formation and cable responses. However, due to limitations of the experimental equipment, the motion of a full-scale system cannot easily be modeled experimentally. Thus, numerical modeling is probably the best way to analyze the dynamic motion of a cable system under strumming excitation. To this end, empirical models have been developed recently in which the fluid oscillation near the cable is represented by a non-linear, self-excited oscillator that is dynamically coupled to the structural member. These models can reproduce the synchronization effect as the shedding frequency approaches the natural frequencies of the structure. The models have been used to simulate the motion of an elastically mounted circular cylinder. The results are in good agreement with experimental data of the maximum amplitude in the resonant or entrained state when the vortex shedding frequency is equal to the natural frequencies of the vibrating cylinder. Studies are underway to couple the models to the equations of motion of a flexible cable to simulate the motion of a cable under vortex excitation. The purpose of this paper is to present the bond graph method as a modeling technique that can incorporate a dynamic model of vortex-induced forces in models of cable systems. Using this method, the response of a complete cable system under various environmental conditions is simulated. In the next section this modeling technique is compared with other cable dynamic modeling techniques. A review of oscillator models then is presented with some examples given to demonstrate the feasibility of the bond graph method as a modeling technique for vortex-induced cable system vibrations. DYNAMIC ANALYSIS OF CABLE-BODY SYSTEMS Since cable-body systems are being used in more and more ocean facilities, there is a strong interest in valid analytical tools which require development of analytical approaches supported by experimental validation. Mathematical modeling and numerical techniques have been used by l 2 3 many investigations.

Enhancing energy harvesting from flow-induced vibration of a semicircular wall via various upstream bluff bodies

Vortex-induced and stall-induced vibrations of a 2D elastically mounted airfoil at high angles of attack in the vicinity of 90° are investigated using a vortex type model. Such conditions are encountered in parked or idling operation at extreme yaw angles provoked by control system failures. At very high angles of attack, massive flow separation takes place over the entire blade span, and vortex shedding evolves downstream of the blade giving rise to periodically varying loads at frequencies corresponding to the Strouhal number of the vortices shed in the wake. As a result, vortex-induced vibrations may occur when the shedding frequency matches the natural frequency of the blade. A vortex type model formulated on the basis of the ‘double wake’ concept is employed for the modelling of the stalled flow past a 2D airfoil. By tuning the core size of the vortex particles in the wake, the model predictions are successfully validated against averaged 2D measurements on a DU-96-W-180 airfoil at high angles of attack. In order to assess the energy fed to the airfoil by the aerodynamic loads, the behaviour under imposed sinusoidal edgewise motions is analysed for various oscillation frequencies and amplitudes. Moreover, stall-induced and vortex-induced vibrations of an elastically mounted airfoil section are assessed. The vortex model predicts higher aeroelastic damping as compared with that obtained using steady-state aerodynamics. Excessive combined vortex-induced and stall-induced edgewise vibrations are obtained beyond the wind speed of 30 m s−1. Copyright © 2014 John Wiley & Sons, Ltd.

Vortex-induced vibration is a fluid instability present in many areas, including offshore platforms, wind turbines, and turbomachinery. The vortices due to secondary flows exert an periodic unsteady force on the elastic structure, leading to potentially dangerous vibrations. Under certain circumstances, the shedding frequency can lock into the structure natural frequency and lead to limit cycle oscillations. These high amplitude vibrations can cause material fatigue, and are a common source of structural failure. This work uses a frequency domain, harmonic balance, CFD code to predict the lock-in of an airfoil at very high angles of attack. The natural shedding frequency is found using a delta phase per iteration method, and the lock-in region is identified by enforcing airfoil motion at different oscillation amplitudes and frequencies. The numerical results are successfully compared to experimental data from wind tunnel testing on a NACA0012 airfoil at deep stall conditions.

An experimental study on the effects of various geometrical parameters to the characteristics of vortex-induced vibration (VIV) of a splitter plate is presented. The dynamic response of the fluid-structure system was measured using particle image velocimetry and laser telemetry simultaneously. Combined data of these techniques allow the assessment of the variation in the VIV response due to geometrical parameters, such as channel geometry, aspect ratio (AR), and trailing-edge thickness (d) as well as the imprint of the excited vibration mode on the flow. The effects of AR and d were both investigated with three different plate geometries and the effect of channel convergence was studied with a single plate geometry. Measurements were performed over a range of Reynolds numbers (Re). The results show that the vibrational response of the combined fluid-structure system is affected by the VIV instability in all cases. Within the measured Re range, a characteristic stepwise behavior of the frequency of the dominant vibration mode is observed. This behavior is explained by the synchronization between the vortex shedding frequency (f0) and a natural frequency (fN) of the fluid-structure system. The results further indicate that this response is modified by geometrical parameters. Channel convergence, i.e., flow acceleration, enhances the vortex shedding, which, in turn, increases the excitation level leading to stronger VIV. Channel convergence does not have a significant effect on f0 or on the dimensionless vibration amplitude (A∕d). An increase of both the number of excited fN’s and the level of synchronization was observed with the lowest AR case. The results also suggest that d is the dominant geometrical parameter. It reduces both the A∕d of the plate and the number of synchronization regions. This stronger effect on the response of the VIV system is due to the direct effect of d on the excitation mechanism.

The application of vortex-induced vibration, characterized by low flow velocity requirements and low costs, has emerged as a prominent focus of research within the domain of ocean-current energy generation. Currently, researchers have primarily conducted detailed investigations into the vortex-induced vibration characteristics of cylinders, with comparatively less attention given to their energy conversion properties. Consequently, this study employs numerical simulations to examine the energy conversion characteristics of a series arrangement of three cylinders, elucidating the vortex-induced vibration response. The findings indicate that the series arrangement of three cylinders can broaden the velocity range for energy harvesting, thereby enabling the cylinders to sustain high-energy conversion efficiency across a wider velocity spectrum. Furthermore, the energy harvesting capacity of the cylinders is predominantly associated with the amplitude and frequency of vortex-induced vibrations. The total energy harvesting power of the three cylinders in series increased with an increase in the reduced velocity, and the maximum power of the three cylinders can reach 5.211 W. In contrast, smaller spacing ratios may affect the energy harvesting efficiency of the vibration. The total energy harvesting capacity of the three cylinders is stabilized at a certain spacing ratio and velocity range; notably, the energy harvesting output of the upstream cylinder closely resembles that of a solitary cylinder. However, at a higher reduced velocity, the energy harvesting power of the midstream cylinder and the downstream cylinder is significantly greater than that of the upstream cylinder.

The present study deals with the shedding process of the Ka´rma´n vortices in the wake of a NACA0009 hydrofoil at high Reynolds number, Reh = 25·103 − 65·103. This research addresses the effects of the foil leading edge roughness on the wake dynamic with a special focus on the vortex shedding frequency, vortex-induced vibration and three-dimensionality of vortex shedding. For smooth leading edge, the shedding frequency of Ka´rma´n vortices occurs at constant Strouhal number, St = 0.24. The wake exhibits 3D instabilities and the vortex induced vibration signals strong modulation with intermittent weak shedding cycles. Direct relation between vibration amplitude and vortex spanwise organization is shown. In the case of rough leading edge, the Ka´rma´n shedding frequency is notably decreased compared to the smooth one, St = 0.18. Moreover, the vortex induced vibration level is significantly increased and the vibration spectra sharply peaked. The occurrence of vortex dislocations is shown to be less frequent with the roughness. The shedding of the vortices is considered on the whole as in phase along the hydrofoil span. Obviously, the shedding process of the Ka´rma´n vortices is highly related to the state of the boundary layer over the entire hydrofoil. It is believed that in the case of smooth leading edge, slight spanwise non-uniformities in the boundary-layer flow lead to slight instantaneous variation in vortex shedding frequency along the span which is enough to trigger vortex dislocations. On the contrary, for the rough leading edge, the location of transition to turbulence is uniformly forced which leads to the reduction of the spanwise boundary-layer non-uniformities and therefore to the enhancement of the coherence length of the Ka´rma´n vortices.

The vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the Reynolds average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k–ε turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse and in-line directions. In previous work, numerical results for the amplitude of oscillation, vortex shedding frequency, and phase angle between lift and displacement were compared to experimental data obtained from Khalak and Williamson (1996) to validate the code for VIV simulations in the transverse direction. In the present work, results are obtained for phase angle, amplitude, frequency, and lift coefficient and compared to experimental data from Jauvtis and Williamson (2003) for an elastically mounted rigid cylinder with two degrees of freedom. Differences in the amplitude of oscillation between experimental and numerical data were observed for both direction. It seems that the fluid flow memory effect is an important aspect that should be taken in consideration on numerical simulation to reproduce the experimental results for VIV with 2DOF as pointed out by Moe and Wu [1].

A broadband electromagnetic type energy harvester for smart sensor devices in biomedical applications

Investigation on the spoiler vibration suppression mechanism of discrete helical strakes of deep-sea riser undergoing vortex-induced vibration

Fluid–structure interaction has been widely studied in the last few decades due to its wide range of applications in engineering fields. This phenomenon plays an important design role, for example, in offshore risers, high slender buildings, chimney stacks and heat exchangers. The vortex shedding generated from a bluff body can induce high-amplitude oscillations, known as vortex-induced vibrations (VIVs). This study presents a numerical analysis to investigate the impact of surface roughness on VIV in the crossflow direction of a circular cylinder. The study also investigates the impact of surface roughness with variation in mass ratio from 2.4 to 11 at a high Reynolds number (Re) = 104 using Reynolds-averaged Navier–Stokes (RANS) equations. The study concludes that roughness on a cylinder results in a reduction in amplitude response. Furthermore, the lock-in region is narrower compared to that of a smooth cylinder, irrespective of the mass ratio. However, it is observed that the impact of surface roughness is more significant in high-mass-ratio cylinders where the lock-in region is more squeezed and shifted toward lower reduced velocities. Furthermore, the vortex mode beyond reduced velocities Ur = 5.84 and 7.52 was observed to be 2S for high and low mass ratios, respectively.