# Hydrodynamic Analysis of Tidal Current Turbine under Water-Sediment Conditions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Particle Phase Model

#### 2.2. Fluid Phase Model

#### 2.3. Blade Element Momentum (BEM) Theory

_{t}is the tip loss factor, F

_{r}is the root loss factor, and ${r}_{\mathrm{h}}$ is the radius of the hub.

#### 2.4. Airfoil

#### 2.4.1. Airfoil Lift Coefficient

#### 2.4.2. Airfoil Drag Coefficient

## 3. Computational Details

#### 3.1. Case Description

#### 3.2. Model Description and Boundary Conditions

#### 3.3. Computational Grids and Grid Independence Study

Mesh Number | Total Number of Cells | Lift Coefficient | Drag Coefficient |
---|---|---|---|

1 | 1,936,784 | 0.92197 | 0.01298 |

2 | 2,577,494 | 0.92566 | 0.01287 |

3 | 3,239,204 | 0.92825 | 0.01282 |

4 | 3,921,914 | 0.92883 | 0.01281 |

**Figure 6.**Computational mesh used in the simulation: (

**a**) domain volume mesh; (

**b**) airfoil surface mesh.

#### 3.4. Numerical Method

^{−5}. The interaction between the discrete and the continuous phases is considered, and the number of continuous phase iterations per DPM iteration is set as 10.

#### 3.5. CFD-DPM Model Validation

#### 3.5.1. Turbulence Model Verification

#### 3.5.2. DPM Model Verification

#### 3.5.3. BEM Model Verification

## 4. Results and Discussion

#### 4.1. Effect of Particle Properties on Airfoil Lift Coefficient

#### 4.2. Effect of Particle Properties on the Airfoil Drag Coefficient

#### 4.3. Effect of Sand on the Power of the 120 kW Tidal Current Turbine

## 5. Conclusions

- (1)
- The CFD-DPM model accurately simulates the airfoil lift and drag coefficients.
- (2)
- When the particle diameter is small, the airfoil lift coefficient surpasses the particle-free lift coefficient. The lift coefficient increases as the particle concentration increases. When the particle diameter and the particle concentration are 20 μm and 100 g/L, respectively, the rotor capture power is increased by at most 2.932% compared to the particle-free case.
- (3)
- When the particle diameter is large, the airfoil lift coefficient is less than the non-particle lift coefficient. The lift coefficient decreases as the particle concentration increases. When the particle diameter and the particle concentration are 2500 μm and 100 g/L, respectively, the 120 kW tidal current turbine power is reduced by at most 21.4% compared to the particle-free case.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Variable Symbols | Definitions |

${U}_{p-fn}$ | The difference between the particle velocity and the particle-free fluid velocity along the particle trajectory of the same Particle ID |

${U}_{fp-fn}$ | The difference between the fluid velocity and the particle-free fluid velocity along the particle trajectory of the same Particle ID |

Time (in the Figure) | Time beginning from the particle injection surface |

Path length (in the Figure) | Path length, defined as the path length of the particle trajectory, which is computed from the particle injection surface |

CFD | Computational Fluid Dynamics |

BEM | Blade Element Momentum |

DEM | Discrete Element Method |

DPM | Discrete Phase Model |

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**Figure 3.**Photo of the sea trial in Zhoushan: (

**a**) 120 kW tidal current turbine; (

**b**) seawater with sediment.

**Figure 4.**Blade profile of the 120 kW tidal current turbine: (

**a**) blade profile; (

**b**) detailed airfoil element section.

**Figure 8.**Erosion diagram of the 120 kW tidal current turbine: (

**a**) the actual erosion diagram under real sea conditions; (

**b**) the simulated erosion cloud diagram at 1.8 m/s (blade contains 30 airfoil elements, the airfoil element at the tip is named “airfoil 30”, and the others are named in sequence. Additionally,

**Er**represents the average erosion rate).

**Figure 10.**Comparison of the simulated turbine power with the experimental data at different flow velocities.

**Figure 11.**The airfoil lift coefficient with the particle diameter under different particle concentrations.

**Figure 12.**The particle trajectories and the fluid streamlines when the particle diameter is 20 $\mathsf{\mu}\mathrm{m}$: (

**a**) the particle trajectories; (

**b**) the fluid streamlines.

**Figure 13.**The particle velocity and the fluid velocity along the trajectory of Particle ID = 5 (particle diameter = 20 $\mathsf{\mu}\mathrm{m}$).

**Figure 14.**The particle velocity and the particle-free fluid velocity along the trajectory of Particle ID = 5 (particle diameter = 2500 $\mathsf{\mu}\mathrm{m}$).

**Figure 16.**The particle velocities and the particle-free fluid velocities along the trajectory of particle ID = 5 under different particle concentrations.

**Figure 17.**The particle trajectories under different particle concentrations: (

**a**) 0.5 g/L; (

**b**) 1 g/L; (

**c**) 1.5 g/L; (

**d**) 2 g/L.

**Figure 18.**The airfoil drag coefficient with the particle diameter under different particle concentrations.

**Figure 19.**The velocities of fluid along the trajectories of Particle ID = 23,000 and Particle ID = 45,000 (1: Particle ID = 45,000 without particles; 2: Particle ID = 23,000 without particles; 3: Particle ID = 45,000 (particle diameter = 2500 $\mathsf{\mu}\mathrm{m}$); 4: Particle ID = 23,000 (particle diameter = 2500 $\mathsf{\mu}\mathrm{m}$)).

**Figure 21.**The variation curves of lift and drag coefficients of airfoil 28 with particle concentration when the particle diameter is 2500 $\mathsf{\mu}\mathrm{m}$: (

**a**) lift coefficient; (

**b**) drag coefficient.

Design Parameters | Value |
---|---|

Rated tidal current velocity | 2 m/s |

Rated rotor rotating velocity | 20 r/min |

Blade number | 3 |

Rotor radius | 5 m |

Hub radius | 0.6 m |

Optimal tip speed ratio | 6 |

Distance Along Pitch Axis (m) | Chord (m) | Twist (°) | Thickness (%) |
---|---|---|---|

0 | 0.460 | 22.5 | 100 |

0.4 | 0.622 | 22.45 | 68.1 |

0.8 | 0.872 | 18.27 | 36.1 |

1.25 | 0.718 | 12.62 | 31.1 |

1.7 | 0.577 | 9.03 | 27.6 |

2.2 | 0.469 | 6.37 | 25 |

2.8 | 0.391 | 4.19 | 22.2 |

3.4 | 0.326 | 2.61 | 21 |

3.8 | 0.268 | 1.64 | 21 |

4.2 | 0.241 | 0.54 | 21 |

4.4 | 0.152 | 0 | 16 |

Minimum Diameter | Maximum Diameter | Median Diameter | Mean Diameter |
---|---|---|---|

$5\times {10}^{-7}$ m | $2.84\times {10}^{-4}$ m | $4.2\times {10}^{-5}$ m | $1.2\times {10}^{-5}$ m |

Liquid Property | |

Density, (Kg/m^{3}) | 1040 |

Temperature, (°C) | 25 |

Viscosity, (Kg/(m s)) | 0.00115 |

Solid Property | |

Material | sand |

Density, (Kg/m^{3}) | 2650 |

Operating Parameters | d_{P} $\left(\mathsf{\mu}\mathbf{m}\right)$ | C_{P} (g/L) | α (°) | c (m) | U (m/s) |
---|---|---|---|---|---|

Effect of particle properties | 20∼3000 | 0.5~2 | 6 | 1 | 16 |

**Table 7.**The power of the 120 kW tidal current turbine at different particle concentrations when the particle diameter is 2500 $\mathsf{\mu}\mathrm{m}$.

Particle Concentration/(kg/m^{3}) | Power/(W) | (P_{0} *-P)/P_{0} * |
---|---|---|

0 | 96,710 | 0 |

2 | 96,206 | 0.521% |

5 | 95,432 | 1.32% |

20 | 92,277 | 4.58% |

40 | 87,674 | 9.34% |

80 | 80,874 | 17.5% |

100 | 76,020 | 21.4% |

_{0}: rotor capture power without particles.

**Table 8.**The power of the 120 kW tidal current turbine at different particle concentrations when the particle diameter is 20 $\mathsf{\mu}\mathrm{m}$.

Particle Concentration/(kg/m^{3}) | Power/(W) | (P_{0} *-P)/P_{0} * |
---|---|---|

0 | 96,710 | 0 |

2 | 96,764 | 0.0558% |

5 | 96,835 | 0.129% |

20 | 97,176 | 0.482% |

40 | 97,411 | 0.725% |

80 | 98,397 | 1.744% |

100 | 99,546 | 2.932% |

_{0}: rotor capture power without particles.

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## Share and Cite

**MDPI and ACS Style**

Gao, Y.; Liu, H.; Lin, Y.; Gu, Y.; Ni, Y.
Hydrodynamic Analysis of Tidal Current Turbine under Water-Sediment Conditions. *J. Mar. Sci. Eng.* **2022**, *10*, 515.
https://doi.org/10.3390/jmse10040515

**AMA Style**

Gao Y, Liu H, Lin Y, Gu Y, Ni Y.
Hydrodynamic Analysis of Tidal Current Turbine under Water-Sediment Conditions. *Journal of Marine Science and Engineering*. 2022; 10(4):515.
https://doi.org/10.3390/jmse10040515

**Chicago/Turabian Style**

Gao, Yanjing, Hongwei Liu, Yonggang Lin, Yajing Gu, and Yiming Ni.
2022. "Hydrodynamic Analysis of Tidal Current Turbine under Water-Sediment Conditions" *Journal of Marine Science and Engineering* 10, no. 4: 515.
https://doi.org/10.3390/jmse10040515