Numerical Simulation on VIV Energy Harvesting of Four Cylinders in Close Staggered Formation with Different Mass Ratios

Nowadays, the demand for marine renewable and clean energy from fluid flow in the oil and gas industry has made electricity the most sought-after and indispensable source of uncontrollable power worldwide. Vortex-Induced Vibrations (VIV) energy harvesting is a promising technology in harnessing energy from flowing water bodies. This study focuses on numerically investigating the VIV of rigid circular cylinders as a sustainable energy source, utilizing a Vortex-Induced Vibration Aquatic Clean Energy (VIVACE) converter to harvest energy from the ocean. Specifically, the research explores the vibration behavior of closely arranged cylinders with different mass ratios, both at low and high values. The study aims to understand the effects of mass ratios on the VIV converter’s performance with four cylinders in close staggered formation. The power conversion of the VIV energy converter model with varying mass ratios (ranging from 2.36 to 12.96) is thoroughly examined, with simulations conducted at a Reynolds number of 82000. The results demonstrate that the maximum converted power peaks at 7.48 W for a mass ratio of 2.36, whereas a higher mass ratio of 12.96 only yields 4.33 W. This emphasizes the significant impact of lower mass ratios in enhancing the power generation from VIV. Overall, the findings of this research provide essential insights to optimize the layout of VIVACE converters in a close staggered array, facilitating the efficient harvesting of energy from flowing water bodies for sustainable and clean energy resources.


Introduction
Vortex-Induced Vibrations (VIV) is a crucial phenomenon observed in the offshore industry, characterized by hydrodynamic forces shedding vortices that excite and interact with flexible structures.This interaction leads to a nonlinear flow structure phenomenon, which has significant implications across various engineering disciplines, including civil, ocean, subsea, mechanical, and aerospace engineering [1].Numerous numerical and experimental studies, along with comprehensive review papers, have already been conducted to investigate into the complexities of VIV [2]- [5].The wide array of issues generated by VIV has driven extensive research in this area.The implications of VIV can be far-reaching, impacting the design and operation of offshore structures and other flexible systems.2023) studied that a Reynolds number of 80 was successfully suppress the wake [11].It provided the small control cylinder situated in the near-wake (downstream) of the main cylinder [12].
Instead of the approaching to suppress the vibrations, VIV will be converted into a useful energy source [13].Hence, a device was created in engineering industry in order to overcome the problem [14] to harness the large amounts of renewable power available in the ocean and other sources of water.The most challenging in today's economy and technically dire in oil and gas industry is to provide adequate energy in the industry for its economic growth while minimizing environmental impact.VIVACE converter is one of the device invented by), The VIVACE converter, conceived by Bernitsas et al. (2006, was designed with the aim of optimizing vortex shedding, as opposed to suppressing it and making use of it rather than reducing it [15].VIVACE converter converts ocean energy into electrical energy.Specifically, wind, tide, solar, ocean wave, and mechanical vibration may all be used to create energy.VIVACE is a model converter capable of generating energy with a high-power conversion efficiency, even from currents as slow as 0.25m/sec which enabling the mass use of ocean and river current energy and enhancing its economic potential.Large numbers of converters are put together to create the array of VIVACE converters in a high-power configuration, as illustrated in Figure 1.

Figure 1. A schematic of VIV power generation [16]
The power generated from the water current, as mentioned by Zahari & Dol (2014), not only comes from a renewable source but also prioritizes environmental friendliness when supplying energy to the offshore platform [17].The power consumption on the offshore platform is significantly higher due to the increased demand during maintenance activities, requiring constant and reliable electrical services to operate continuously.This is particularly critical for unmanned platforms that heavily rely on machines for their operations.
The aim of this research is to understand the effect of the mass ratio on the vibration synchronization for VIV energy converter model.This research focuses more on the harvested energy of the VIV for four cylinders with various range of mass ratios using Computational Fluid Dynamics (CFD) approaches.In this research, the utilization of multiple cylinders was explored, as it proved to be more effective than a single cylinder in generating power.When these cylinders are appropriately constructed, energy harvesting from a configuration of four staggered cylinders with varying masses is significantly influenced by differences in wake energy.

Geometrical Modelling and Boundary Condition
In this study, Figure 2 depicts the presence of four cylinders referred to as C-1, C-2, C-3, and C-4.C-3 and C-4 are positioned in a slightly staggered manner, symmetrically flanking C-1 and C-2.The simulation primarily concentrated on a Single Degree of Freedom (SDOF) system.The elastic system comprises a damping constant, denoted as 'c,' and a spring damper, represented by 'k.' Table 1 provides the specific physical parameter values employed in the current model.At the inlet boundary, the average speed of the consistent flow was associated with a Reynolds Number equal to 82000.Reynolds number, damping ratio and spring stiffness will be a constant variable for the multiple cylinders model with different range of mass ratios.The mass ratio and reduced velocity are important parameter that dominates the VIV responses.It is defined as Equations (1) and Equation (2), respectively.
(1) where m (mass per unit length), reduced velocity as defined by Summer and Fredsoe (1997) the ratio of the cylinder's wavelength to its diameter in the trajectory of the cylinder [18]- [19], respectively and   is the water frequency at which a cylinder vibrates naturally [20] To evaluate the energy transfer of the cylinder, a one cycle's supply of energy gained from the cylinder's flow is defined as Equation ( 3) and Equation (4).
where  is the spring stiffness,  is the amplitude of the waves,   is coefficient of damping in a system,   is the cylinder's vibration frequency and the flow of VIV power is evaluated throughout an oscillation cycle [20].
The boundary conditions within the domain have been in Table 2. To model the pressure outlet boundaries, slip walls were employed to guarantee that there was no shear stress between the fluid and the walls.Viscous stress was not taken into account at the outlet.It's worth noting that a time step of 0.05 seconds was implemented, ensuring adequate stabilization for the solution.

Mesh Independence Study
Figure 3 illustrates the computational meshes configurations of a cylinder for simulation domain.As seen in the graph in Figure 4, the simulations began to converge around Ay/D = 0.9382 at 100 000 to 130 000 number of elements.A satisfactory correlation is observed between the obtained amplitude response data.3. The graph in Figure 6 reveals a strong correlation between the acquired results and the basis for comparison.The validation error was found to be less than 5%.Notably, the graph demonstrates that increasing the lower velocity significantly reduces the cylinder's amplitude, as indicated by the numerical calculation results [20].

Results and Discussion
Figure 7 presents amplitude ratio for the four cylinders with different mass ratios.It is important to emphasize that the primary focus of the current research is on investigating the effect of mass ratios.The disturbed flow from C-1 and the cylinders on the side, C-3 and C-4 significantly impacts the velocity of cylinder that is located lower down the line (C-2) when the cylinders are arranged extremely close together.When comparing the VIV reaction of the cylinders with high mass ratio to those with a low mass ratio, there are noticeable differences due to the mass ratio [21].The effect of the various mass ratios on the vibrations of the four cylinders of the VIV waves is thoroughly investigated by conducting the VIV numerical simulation of mass ratio range 2.36-12.96.At low mass ratio resulted the higher Experiments, numerical modelling, and analytical modelling have all recently been used to enhance the understanding of VIV.Wang et al., (2020), Han et al. (2021), Goncalves et al. (2012), and Williamson & Govardhan (2008) are just a few examples among the individuals who contributed to this research [3]-[7].VIV occur naturally and by forced oscillations at velocities and amplitudes which known as selfexcited oscillations and forced oscillations (vibration-induced vortices) [8]-[10].Min et al. (

Figure 2 .
Figure 2. Schematic drawing of the four cylinders (not to scale)

Table 2 :
The boundary Condition of the Present Model Type of

Figure 3 .
(a) Computational domain meshes of a cylinder.(b) Illustration of close-up mesh

Figure 4 .
Figure 4. Mesh independence test result for present computational model 2.3.Model Validation The arrangement and computational meshes of four cylinders are illustrated in Figure 5.The validation of present model was carried out based on Zhang et al. (2018).The physical parameters required for conducting the validation are presented in Table3.The graph in Figure6reveals a strong correlation between the acquired results and the basis for comparison.The validation error was found to be less than 5%.Notably, the graph demonstrates that increasing the lower velocity significantly reduces the cylinder's amplitude, as indicated by the numerical calculation results[20].

Table 1 .
Physical Parameter for Present Model