Modal and Static Analysis of Vortex Bladeless Wind Turbines with Different Geometries

. The renewable energy industry has undergone remarkable growth in recent times, with wind energy assuming a preeminent role as a source of clean energy. Five distinctive geometries were analyzed, including a traditional circular form, a decagonal form, and three sinusoidal forms to evaluate the modal and structural characteristics of vortex bladeless wind turbines. The ANSYS software was employed to carry out both the modal and structural analysis. The vortex bladeless rod was firmly fixed and the mast was exposed to a wind pressure of 15 Pa during modal analysis. The structural analysis was executed to compute the deflection of the vortex bladeless wind turbine under the same wind pressure. The results demonstrated that the sinusoidal forms exhibited the greatest deflection at a wind speed of 5m/s. These findings possess the potential to optimize and augment the design of vortex bladeless wind turbines, provide guidance for future design decisions, and boost the efficiency and dependability of these wind turbines. It is therefore posited that the consideration of diverse geometries in the design of vortex bladeless wind turbines is of paramount importance, and the findings of this study are expected to be of great use to engineers and designers in the wind energy field, thereby catalyzing the progression of this thriving renewable energy source.


Introduction
The quest for clean and sustainable energy sources has led to a surge in research and development of innovative solutions for harnessing wind energy.Conventional wind turbines have been the go-to solution for many years, but they come with their own set of limitations, such as high maintenance costs, large physical footprint, and potential environmental impacts.To address these limitations, a new and innovative approach has emerged in the form of Vortex Bladeless Wind Turbines (BWT).BWT is a novel technology that harnesses the energy of vortices generated by the airflow over a cylindrical structure.The technology is based on the concept of vortex-induced vibration, where the structure starts vibrating and reaches resonance as the wind strength increases, leading to the generation of electricity through an alternator and a tuning system.The energy captured by the BWT is derived from a phenomenon of vorticity, known as the vortex-shedding effect.This technology has the potential to revolutionize the wind energy industry, offering a more efficient, cost-effective, and environmentally friendly solution.However, to ensure the widespread implementation and success of BWT, a comprehensive understanding of its performance is necessary.In this regard, modal and static analysis, along with aerodynamic studies, play a critical role in determining the performance of BWT.This research paper aims to conduct a comparative study of the modal and static behavior of BWT with different geometries, taking into consideration the aerodynamic behavior of the structures.The results of this analysis will provide valuable insights into the performance of BWT and assist in optimizing its design for improved performance.The methodology section of this paper will describe the methods used for modal and static analysis, as well as the aerodynamic studies conducted.The results and discussion section will present the findings of the analysis and provide an in-depth discussion of the implications of the results.The conclusion section will summarize the main findings and suggest avenues for future research in this field.

Literature Review
The study of Vortex Bladeless Wind Turbine (BWT) technology has been the focus of substantial research efforts in recent years, as scientists seek to enhance its design and operational efficiency [1].The purpose of this literature review is to provide a comprehensive examination of existing research on Vortex Bladeless Wind Turbines, including the underlying principles of the technology, the current state of modal and static analysis methods and aerodynamic studies, and the development of the technology to date.The principle behind the Vortex Bladeless Wind Turbine technology is the harnessing of wind energy through the vortex-shedding effect, which refers to the generation of cyclical patterns of vortices as the wind passes over a structure.These resonant vibrations of the structure are then leveraged to produce electricity.As elucidated by G.R.S. Assi [2], the vortex shedding effect can be effectively captured through the utilization of a cylinder fixed vertically on an elastic rod, as opposed to the conventional wind turbine components of a tower, nacelle, and blades.To optimize the design and performance of Vortex Bladeless Wind Turbines, various methods of modal and static analysis have been developed.The modal analysis provides insight into the dynamic behavior of the structures, including the identification of natural frequencies and modes of vibration [3].Conversely, static analysis characterizes the behavior of the structures under steady-state conditions [4].The integration of both modal and static analysis is crucial in optimizing the design of the Vortex Bladeless Wind Turbine structures, as they impart valuable information on the behavior of the structures under different operational circumstances.Aerodynamic studies are a crucial aspect of understanding the performance of Vortex Bladeless Wind Turbine structures.These studies examine the airflow around the structures and offer critical information on the interaction between the structures and the surrounding air [5].This information is essential for enhancing the design of Vortex Bladeless Wind Turbine structures and ensuring their effective deployment.Studies have been conducted to optimize the design of Vortex Bladeless Wind Turbine structures, including examinations of various geometries, materials, and tuning systems [6].The results of these studies demonstrate that the design of the Vortex Bladeless Wind Turbine structures has a significant impact on their performance, and additional research is required to further optimize their design and ensure effective deployment [7].
In conclusion, the literature review provides an extensive overview of existing research on Vortex Bladeless Wind Turbines, including the underlying principles of the technology, the current state of modal and static analysis methods and aerodynamic studies, and the development of the technology to date.As underscored by the literature, there remains a pressing need for further research to optimize the design and ensure the effective deployment of Vortex Bladeless Wind Turbines.

Geometric & Material Specification
The Vortex-Induced Vibration Bladeless is a device that utilizes the natural frequency of a lightweight composite material, such as fiberglass or nylon, to generate oscillations at low wind speeds.Figure 1 presents a front and top view illustration of the device, while Table 1 summarizes its dimensions.The mast and rod have lengths of 2000 mm and 225 mm, respectively, with upper and lower diameters of 200 mm and 75 mm.The use of fiberglass and nylon for the mast and grounded rod is due to their favorable properties, including low lift force requirement and acceptable tensile and compressive strength as shown in Table 2.  Thickness 3 Furthermore, these materials can be easily deformed into various shapes, eliminating the need for additional machining processes.This recent study analyzed five different shapes, as depicted in Figure 2, all with the same diameter and modeled using the equations listed in Table 3.

Mesh Topology
The methodology of mesh generation in the realm of finite element analysis (FEA) of a Bladeless Wind Turbine is a crucial aspect for obtaining accurate and trustworthy results.The mesh, consisting of small constituents known as finite elements, serves as a computational representation of the wind turbine's geometry.These finite elements are utilized to approximate the wind turbine's response to various operating conditions.The meshing process commences with the creation of a computer-aided design (CAD) model of the wind turbine, which defines its geometry.Following this, a three-dimensional mesh is generated using meshing software to divide the CAD model into finite elements as depicted in Figure 3.The size, shape, and distribution of these elements must be meticulously selected to ensure that they are fine enough to capture essential details of the wind turbine, yet coarse enough to maintain computational feasibility.The mesh generation process is indispensable in guaranteeing the validity and reliability of the

Boundary Conditions
The modal analysis of the Vortex Bladeless Wind Turbine was conducted by fixing the vortex bladeless rod while the mast was subjected to a pressure of 15 Pa, as depicted in Figure 4, utilizing the ANSYS Workbench 21.1 software.A structural analysis was performed to determine the deflection of the Vortex-Induced Vibrations (VIV) bladeless wind turbine.The boundary conditions were consistent across all geometries.The value of the pressure was determined through the application of Equation 1.
where P is the pressure, F is the force, and A is the cross-sectional area.
F is the dynamic drag force, ρ is the density of the fluid, u is the velocity of the fluid, and DLC is the characteristic dimension of the body.This equation represents the dynamic drag force experienced by a body moving in a fluid.
represents the area of a cylinder with radius "r" and length "l"

Results & Discussion
The results of the modal and static analysis of the vortex bladeless wind turbine with five different geometries have been presented and discussed in this paper.The geometries comprised of conventional circular, decagonal, and sin wave shapes, each of which were generated using mathematical equations.The modal and static analysis was , 01 (2023) E3S Web of Conferences ICMPC 2023 https://doi.org/10.1051/e3sconf/202343001254254 430 performed using ANSYS Workbench 21.1 as illustrated in Figure 5-9.The results showed that the geometries generated using sin wave equations resulted in the highest deflection at a wind speed of 5m/s as shown in Table 4.The findings of this study provide valuable insights into the impact of geometry on the deflection of vortex bladeless wind turbines.The results demonstrate the significance of the geometry in influencing the response of the wind turbine and thus, it is recommended that future studies consider the geometry as an important factor in the design of these types of turbines.Additionally, the results obtained from this study can be used as a reference for engineers and designers in the wind energy industry.The findings highlight the importance of considering the geometry of the wind turbine in order to optimize its performance and reduce deflection under various wind speeds.

Conclusion
In conclusion, the study aimed to assess the performance of different geometries in a vortex bladeless wind turbine.Modal and static analysis were conducted on five different geometries, including conventional circle, decagon, and sin wave geometries.The results showed that the sin wave geometry displayed the highest deflection at a wind speed of 5m/s.The findings of this study are significant in guiding the future design of vortex bladeless wind turbines, particularly in choosing the appropriate geometry for maximum deflection, which ultimately translates to improved energy generation.It is recommended that future studies be conducted to further assess the performance of the vortex bladeless wind turbine, especially in a real-world setting.This would provide valuable insights into the feasibility of using the vortex bladeless wind turbine as a renewable energy source and enable the optimization of its design.In conclusion, this research has demonstrated the importance of geometry selection in improving the performance of vortex bladeless wind turbines and highlights the need for further research in this area. .

Table 2 :
Material Properties

Table 4 :
Comparisons of Modal and Static Analysis of all BWT Geometries