# Design and Development of Bladeless Vibration-Based Piezoelectric Energy-Harvesting Wind Turbine
## 3 Computational Fluid Dynamics (CFD) Simulation Results  
The work in this part is targeted at applying a computational fluid dynamics (CFD) approach to simulate vortex-induced vibrations of the flexible rising rods (mast). The current CFD capabilities may produce results that are reasonably close to the experimental data and may be used to calibrate existing low-order analytical models and provide a generic framework for various flow characteristics and boundary conditions. CFD flow models of numerous hollow mast designs were examined based on a theoretical review of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ITEM No.** & **Part Name** & **Description** & **Quantity** & **Material** \\ \hline
1 & Base & H 182 mm; L 455.24 mm; W 455.24 mm & 1 & Steel grade A36 \\
2 & Elastic Rod & H 1202.6 mm; D 32.28 mm & 1 & Carbon fiber–reinforced polymer \\
3 & Hollow Mast & H 2194.5 mm; OD 300 mm; ID 280 mm & 1 & Carbon fiber–reinforced polymer \\
4 & Alternator & H 48.54 mm; OD 247.32 mm; ID 203.7 mm & 2 & Electromagnetic coil \\
5 & Stator & H 203.68 mm; D 143.79 mm & 1 & Carbon fiber–reinforced polymer \\
6 & Stator Support & H 2203.18 mm; D 123.54 mm & 1 & Carbon fiber–reinforced polymer \\
7 & Hollow Mast Base & H 512.95 mm; OD 262.32 mm; ID 123.54 mm & 1 & Carbon fiber–reinforced polymer \\
8 & Anchor Support & H14.57 mm; OD 44.57 mm; ID 23.67 mm & 4 & Steel grade A36 \\
9 & Inner Ring & H 175.21 mm; OD 254.29 mm; ID 207.48 mm & 1 & Magnet \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The proposed design components and specifications. Figure 2: The proposed design with locations of piezoelectric sensors. these designs. CFD is utilized to visualize the flow patterns, while the experimental work is conducted to be able to measure the amount of harvested energy, in addition to verifying the CFD results. The following section describes the wind flow trajectories and pressure distribution on the hollow mast. Different hollow mast designs with various diameters and heights were explored, and CFD results are presented in this section. Based on the experimental results, which showed that 15 m/s is the airflow speed where a good amount of energy can be generated, a lower wind speed of 10 m/s and a higher wind speed of 20 m/s were chosen to focus on in addition to 15 m/s. The step size of 5 m/s was chosen based on that fact that there is no significant change when the speed step size is smaller than that. In Appendix A, Tables A1-A4 display the experimental results with a step size of 1 m/s, which proves that there is no significant change when the step size is small. The convergence criterion should be the first thing to check the convergence of the executed simulation. It helps in understanding the global and local imbalances in an iterative way in a CFD simulation. In this paper, residuals that represent the solution imbalances were considered as the convergence criterion to check for numerical accuracy. Residuals are expected to be as small as possible to indicate the accuracy of simulations. Residuals below \(1\times 10^{-3}\) were taken as a good starting point to move to the next check. The results of the CFD simulations for two different geometries (simple cylinder and complex cylinder) at a wind speed of 10 m/s are presented. Figure 3 shows the vorticity contours for simple cylinders and complex cylinders, respectively. It can be noticed that the complex cylindrical shape produced more flow disturbance and intensive vortices. This essentially motivates the mast to vibrate and, hence, produce energy. Figure 3 below shows CFD simulation results and a comparison of two different shape designs. In addition, the velocity, pressure, and vorticity contours for both the simple cylinder and modified cylinder designs at wind speed equal to 10 m/s were investigated and are presented in Figure 3. CFD simulations revealed that the modified cylinder design at low wind speed yields no difference from the simple cylinder design.