# Numerical Analysis of a Horizontal Pressure Differential Wave Energy Converter

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Modeling

#### 2.1. Continuity, Momentum, and Volume Fraction

^{3}) is the density of the fluid, $v$ (m/s) is the velocity, $P$ (Pa) is the pressure, $g$ (m/s

^{2}) is the acceleration due to gravity, $\mu $ is the dynamic viscosity (Pa s), $t$ (s) is the time.

^{3}). The surface tension force is expressed as a volume force and is added to the momentum equation as a source term.

^{3}) is:

- Laminar flow
- Regular gravity waves
- Shallow water
- Two-dimensional geometry

#### Boundary Conditions

#### 2.2. Performance Assessment

^{3}/s) is the flowrate through the pipe. The available wave power per unit width can be determined by:

#### 2.3. Pressure Resource

^{3}) is density, $H$ (m) wave height, $\kappa $ (m

^{−1}) is wave number, $h$ (m) is water depth, and $z$ (m) is the depth of device measured from the free surface. Combining Equations (11) and (12), the maximum pressure difference between two points is achieved, when one point is under the crest and the other point is under the trough of the wave i.e., the distance between two points is half or any multiple of the half of the wave length. However, in the presence of a submerged body, the pressure field will be modified due to the diffraction pressure which is the component of pressure due to the presence of a body, and the radiation pressure which is due to the power absorbed or radiated back to the wave due to the body motion. The CFD modeling allows the inclusion of the effects of diffraction and radiation in the pressure calculation.

## 3. Results and Discussion

#### 3.1. Model Setup and Validation

#### 3.2. Flow Dynamics in the Wave Energy Extraction Device

#### 3.3. Performance Characteristics

## 4. Conclusions

- The CFD model used for simulating the wave conditions has been successfully validated against free surface elevation data from the published literature.
- The concept of a differential pressure-driven wave energy device has been proven by numerical simulation.
- Simulation results show that the efficiency of the device decreases with the wave height but increases significantly with the wave time period.
- A higher power take-off (PTO) damping also increases the efficiency of the device.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The new concept of wave energy extraction by forcing water flow through a submerged pipe. An orifice plate is used to represent the effects of turbine damping.

**Figure 2.**(

**a**) Mesh distribution in the computation domain (

**top**). Meshes are concentrated inside the orifice (

**bottom**). (

**b**) Flow chart indicating the CFD methodology.

**Figure 3.**Water surface elevation at (

**a**) WG3, (

**b**) WG4, and (

**c**) WG5 showing the comparison between the present CFD prediction and Rezanejad et al.’s [13] experiment for the case of the time period, $T=1$ s and wave height, $H=0.02$ m. WG3, WG4, and WG5 are located at 8.65 m, 8.95 m, and 9.35 m from the wave generator.

**Figure 4.**(

**a**) Contour plots of volume fraction of water show the structure of the wave, (

**b**) Contour plots of axial velocity showing reversing flow through the submerged pipe.

**Figure 5.**Effects of wave height on the (

**a**) pressure drop across the pipe (

**b**) velocity through the orifice.

**Figure 6.**Effects of orifice size on the (

**a**) pressure drop across the pipe (

**b**) velocity through the orifice.

**Figure 7.**Effects of time period on the (

**a**) pressure drop across the pipe (

**b**) velocity through the orifice.

**Figure 8.**The efficiency of the wave energy devices for different time periods and damping conditions against wave height.

Length (m) | 10 m |
---|---|

Diameter (m) | 0.1 m |

Orifice opening (mm) | 1 mm, 2.5 mm |

Mesh Elements | (Normalized Surface Elevation)_{CFD}/(Normalized Surface Elevation)_{Expt} |
---|---|

31,500 | 1.2 |

42,000 | 1.15 |

112,500 | 1.12 |

375,000 | 1.08 |

450,000 | 1.04 |

860,000 | 1.02 |

1,120,000 | 1.005 |

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**MDPI and ACS Style**

Renganathan, M.; Hossain, M.
Numerical Analysis of a Horizontal Pressure Differential Wave Energy Converter. *Energies* **2022**, *15*, 7513.
https://doi.org/10.3390/en15207513

**AMA Style**

Renganathan M, Hossain M.
Numerical Analysis of a Horizontal Pressure Differential Wave Energy Converter. *Energies*. 2022; 15(20):7513.
https://doi.org/10.3390/en15207513

**Chicago/Turabian Style**

Renganathan, Manimaran, and Mamdud Hossain.
2022. "Numerical Analysis of a Horizontal Pressure Differential Wave Energy Converter" *Energies* 15, no. 20: 7513.
https://doi.org/10.3390/en15207513