# Numerical Simulation of an Oscillatory-Type Tidal Current Powered Generator Based on Robotic Fish Technology

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

**F**is the body force and $p$ is the pressure:

^{4}, because the oscillator size against the flow is 0.15 m. A uniform flow field with Vx = 0.5 m/s (flow from the left side—x direction) is used in all of the following calculations [9].

## 2. Study on an Airfoil-Type Oscillator

^{8}to 5 × 10

^{4}Pa to investigate the change of $Cl$, details of the simulation conditions are provided in Table 1.

^{8}Pa, there is almost no deformation; however, when E = 10

^{6}Pa, the maximum $Cl$ is obtained, where $Cl$ is approximately three times greater. However, the $Cl$ will also drop when the value of E is decreased. Therefore, it can be concluded that the optimum elastic modulus is E = 10

^{6}Pa for this shape of foil, in the case of different cambers the optimum value of E will most likely vary.

^{4}, 10

^{6}Pa, and 10

^{8}Pa has been examined, providing an optimal $Cl$ value for E = 10

^{6}Pa. The scale in the y direction is scaled up as the deformation is very small. E = 10

^{8}is not shown here, as the deformation is insignificant. Instantaneous deformations of the foil for E = 5 × 10

^{4}and E = 10

^{6}are shown in Figure 4 and Figure 5, respectively. It is recognized that, compared to the case of E = 5 × 10

^{4}, in which the body curves with more than one center of curvature, in the case of E = 10

^{6}, the foil is singularly concave or convex, providing an asymmetric foil. This forms an attack angle for the foil, and is the reason for the increase of $Cl$.

^{6}Pa; the lift will decrease with any increase or reduction of the value of E.

^{6}Pa. The $Cl$ is three times that of the previous y = 0.001 sin(2πt) m. However, the calculation failed due to the occurrence of negative meshes when a larger displacement was used. The authors will investigate the reason for this in future research.

## 3. The Optimum Shape of a Reciprocating Oscillator for Self-Induced Oscillation

#### 3.1. The Pre-Test in 2D

#### 3.1.1. Reason for a Higher $Cl$ Value in the Case of a Semicircle

#### 3.1.2. Reason for Increasing Instability with Elongation

#### 3.1.3. Finding a Model with Optimal Length in the x-Direction

#### 3.1.4. 3D Fluid-Structure Coupled Analysis

## 4. Conclusions

- (1)
- An airfoil-shaped oscillator with optimal elasticity effectively increases lift, and we found that the elastic modulus E = 106 Pa is the best for a NACA0015 model foil.
- (2)
- Analysis of the flow field for six common head shapes clearly showed that the discontinuous flow caused by a square-headed oscillator results in higher Cl due to intense vortex shedding. Stable operation can be achieved by selecting the optimum length to width ratio, and this ratio is confirmed to be one (square) by our simulation.
- (3)
- A shape with a higher Cl than the semicircle has been identified, and the efficacy of this shape was confirmed in the fluid-structure coupled analysis.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Deformation in case of E = 5 × 10

^{4}Pa at t = 2.1 s, $Cl$ is reduced at this instant. Scale in y direction is scaled up.

**Figure 5.**Deformation in case of E = 10

^{6}Pa at t = 2.1 s, $Cl$ will increase after this instant. Scale in y direction is scaled up.

**Figure 11.**Distribution of velocity for an extended semicircle (model 3) at t = 15.5 s. Oscillation is unstable.

**Figure 12.**Distribution of vorticity for an extended semicircle (model 3) at t = 15.5 s. Oscillation is unstable.

**Figure 13.**Distribution of velocity for an extended semicircle (model 2) at t = 23.75 s. The reattached region is moving to the rear on the circular side of the object.

Time Step Size for Flow Calc. (s) | 0.005 |

Scale of flow domain (m) | 6 × 3 × 0.1 |

Type of mesh | prism |

Min. size of mesh (m) | 0.007 |

Density of structure (kg/m^{3}) | 1000 |

Length of structure (m) | 1 |

Depth of structure (m) | 0.1 |

Shape | x/y | Max $\mathit{C}\mathit{l}$ to Circle’s | Periodic | Stability | Cd * to Circle | |
---|---|---|---|---|---|---|

1 | 0.5 | 1.53 | good | not good | 1.67 | |

2 | 1 | 1.92 | good | not good | 1.67 | |

3 | 1.4 | 3.2 | detected | Very poor | 1.67 | |

4 | 2.5 | 1.3 | excellent | excellent | 0.5 | |

5 | 1 | 1.53 | excellent | good | 1.67 | |

6 | 1 | 1.97 | excellent | excellent | 1.67 |

Flow time step size (s) | 0.005 |

Flow domain scale (m) | 3 × 2 × 0.1 |

Flow domain mesh type | prism |

Min. size of mesh (m) | 0.017 |

Weight of struc. model (kg) | 1.62 |

Size of model 1 (m) | 0.075 × 0.15 × 0.1 |

Size of model 2 (m) | 0.15 × 0.15 × 0.1 |

Size of model 3 (m) | 0.18 × 0.15 × 0.1 |

Dia. of hole in models (m) | 0.04 |

Elastic base (N/m^{3}) | 48,000 |

Model | Size in x-direc. (m) | Max $\mathit{C}\mathit{l}$ | Max Disp. (m) |
---|---|---|---|

No.1 | 0.075 | 7 | 0.0120 |

No.2 | 0.15 | 8.8 | 0.0213 |

No.3 | 0.18 | 10 | 0.0198 |

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**MDPI and ACS Style**

Yamamoto, I.; Rong, G.; Shimomoto, Y.; Lawn, M. Numerical Simulation of an Oscillatory-Type Tidal Current Powered Generator Based on Robotic Fish Technology. *Appl. Sci.* **2017**, *7*, 1070.
https://doi.org/10.3390/app7101070

**AMA Style**

Yamamoto I, Rong G, Shimomoto Y, Lawn M. Numerical Simulation of an Oscillatory-Type Tidal Current Powered Generator Based on Robotic Fish Technology. *Applied Sciences*. 2017; 7(10):1070.
https://doi.org/10.3390/app7101070

**Chicago/Turabian Style**

Yamamoto, Ikuo, Guiming Rong, Yoichi Shimomoto, and Murray Lawn. 2017. "Numerical Simulation of an Oscillatory-Type Tidal Current Powered Generator Based on Robotic Fish Technology" *Applied Sciences* 7, no. 10: 1070.
https://doi.org/10.3390/app7101070