*5.3. Water Tunnel Simulation*

The water flow around the structure will be simulated using the software's turbulent flow. As mentioned before, this module aims to solve the Navier–Stokes equations but instead of air, we are using water.

The water tunnel dimensions are 70 m in height, 200 m in width and 100 m in depth. The above-mentioned structure is placed inside the tunnel. Only the part of the structure that is subject to the water is inside this water tunnel, as presented in Figure 7.

**Figure 7.** Water tunnel using the software.

The concept of the following simulation is the same as the wind turbine simulation. The goal is to obtain *v*<sup>2</sup> to calculate the power generated by the tidal turbine, as presented in Figure 8.

**Figure 8.** Betz Law.

As depth increases, atmospheric pressure also increases. The deeper you go under the sea, the greater the pressure of the water pushing down on you. For every 33 feet (10.06 m) you go down the pressure increases by one atmosphere. The atmospheric pressure at a depth of 40 m is about 5 atm. The water temperature considered will be 10 ◦C, as it is the average temperature of the water in the chosen place. However, the temperature does not have a considerable effect on the simulation. The average and maximum current speeds were chosen as inputs at the open boundary. Results are on Figure 9.

In the figure above, the resulting water flow is illustrated, being characterized by velocity magnitude, orientation and direction. The velocity magnitude's values are differentiated by colors whose legend can be seen at the right border. This figure is for an input

speed of 1.902 m/s, but several simulations were performed for different current speeds as presented on Table 7.

**Figure 9.** Current Speed (m/s) using the software.

**Table 7.** Values of current speed before and after the rotor.


#### **6. Piezoelectric Materials Simulation**

The piezoelectric effect will be simulated using the software. The piezoelectricity interface combines the solid mechanics and electrostatics interfaces with the constitutive relationships required to model the piezoelectric phenomena. Both direct and inverse piezoelectric effects can be modeled.

The piezoelectric coupling can be formulated using either the strain–charge or stress– charge form. There are three modules within the structural mechanics and acoustics modules branch that offer this feature for simulating piezoelectricity: the acoustics module, MEMS (microelectromechanical systems) and module and structural mechanics module.

The acoustics module includes dedicated tools for modeling wave generation and propagation in fluids, linear elastic materials, porous media and piezoelectric materials. It is used for piezoelectric transducers as transmitters to radiate sound to the surrounding fluids and as receivers to detect sound coming from the surrounding fluids.

The MEMS module includes a terminal feature that allows you to connect a piezoelectric device to an electrical circuit. The electrical circuit can be used to excite the transducer as well as receive detected signals. The terminal feature also enables the computation of the lumped parameters of the piezoelectric device, such as admittance and scattering parameters (S-parameters).

The structural mechanics module provides efficient modeling features such as the shell and membrane interfaces [15].

The simulations will be run by the last module with a geometry as illustrated on Figure 10. This is a finite element analysis (FEA) software package tailored for analyzing the mechanical behavior of solid structures. The structural mechanics module brings built-in multiphysics couplings that include thermal stress, fluid–structure interaction and piezoelectricity [15].

As previously mentioned, the piezoelectric material used is a polyvinylidene difluoride (PVDF) film with an external depth of 13 mm and an external width of 25 mm.

**Figure 10.** PVDF film drawn using the software.

Before any simulation is performed on the piezoelectric material, it is necessary to know the pressure that the wind exerts in the area where the piezoelectric materials will be applied.

The piezoelectric materials will be installed in the area shown in Figure 11.

**Figure 11.** Area where piezoelectric materials will be applied.

The piezoelectric materials will be applied in the pink area shown in the figure because they receive the pressure of the wind, and their operation is not significantly affected by the wind turbines. This area is approximately 108 × 2.62 m.

The wind was calculated at the average height of 54 m using the formula mentioned before in Expression (3). Results are compiled on Table 8.

**Table 8.** Values of wind speed at 54 m.


Several simulations were performed to find out the pressure exerted by the wind on the structure. The pressure exerted on the tower with a wind speed of 7.30 m/s is shown on Figure 12 and all the results are compiled in Table 9.

**Figure 12.** Pressure (Pa) using the software.

**Table 9.** Values of pressure according to wind speed.


Knowing the pressure that the wind exerts on the structure, we were able to extract the current density and voltage of the piezoelectric material, presented on Table 10. Therefore, the simulation input is the pressure that we received from the previous simulations.

**Table 10.** Values of voltage and current.


Figure 13 shows the behavior of the piezoelectric material when the wind pressure is exerted.

**Figure 13.** PVDF film stress using the software.
