# Hydrodynamic Performance Analysis of the Vertical Axis Twin-Rotor Tidal Current Turbine

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Definition of Coordinate System and Dimensionless Parameters of Turbine

## 3. Computational Fluid Dynamics (CFD) Setup and Mesh

^{−4}. CFX uses the SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm [33] in the pressure-velocity coupling, therefore, several iterations were required within each timestep to make sure that the mass is conserved and the results are trustworthy. In the transient simulation presented in this manuscript, the transient solver is set to at least two times iteration within each timestep. The maximum number of coefficient loops should be less than 10 within each timestep. Adaptive timesteps were chosen resulting in an adjustable timestep with target coefficient loops between three and five iterations. The timestep was set to a maximum timestep of 1.0 × 10

^{−3}s. A detailed discussion of the timestep can be seen in Section 4.1.2. The high-resolution second-order backward Euler scheme is adopted to discretize the transient term, ensuring an implicit time discretization. Time discretization adopted first-order discrete format.

## 4. Numerical Research on the Performance of Vertical Axis Twin-Rotors Tidal Current Turbine

#### 4.1. Numerical Verification of CFD Simulation

#### 4.1.1. Numerical Verification of Mesh Independence

_{q}can be obtained by Equation (15). Figure 6 shows the torque coefficient of the single turbine with three different mesh qualities. As we can see, the torque coefficient curve of mesh 1 is different from the other curves when the phase angle is between 150°~210°. The torque coefficient of mesh 2 and mesh 3 is almost the same. Therefore, mesh 2 has already reached the requirements of mesh independence and mesh 2 was adopted in the following numerical simulation.

#### 4.1.2. Numerical Verification of Timestep

#### 4.1.3. The Effects of Side Wall and Wall Category

_{w}(distance between the side wall and center of the turbine) on the hydrodynamic performance of the turbine is investigated in this paper.

_{w}, namely 0.75D, 1D, 2D, 4D, 8D, are chosen to investigate the influence of side wall effects on the hydrodynamic performance of the turbine. Two different wall categories are chosen to investigate the influence of wall category on the hydrodynamic performance of the turbine. Figure 8 and Figure 9 shows the torque coefficient of a slip wall and a non-slip wall at different D

_{w}. As Figure 8 and Figure 9 shows, the peak value of torque coefficient decreases with the increase of D

_{w}. Deviation of torque coefficient is very big when D

_{w}is less than 6D. The torque coefficient curve is almost the same when D

_{w}is 6D and 8D, respectively. Therefore, when the distance between side wall and center of the turbine is bigger than 6D, the effects of side wall can be neglected. Figure 8 and Figure 9 shows the average C

_{q}curve of the turbine with a slip wall and non-slip wall at different D

_{w}. As Figure 9 shows, the C

_{q}curve is almost the same when the D

_{w}is bigger than 6D. Therefore, we can draw a conclusion that the effects of different wall categories can be neglected at certain conditions. In order to minimize the influence of the side wall on the hydrodynamic performance of turbine, we recommend that the distance between the side wall and the center of the turbine should be larger than 6D.

#### 4.1.4. Comparison between Numerical Simulation and Model Experiments

#### 4.2. The Analysis of the Hydrodynamic Characteristic of the Vertical Axis Twin-Rotors Tidal Current Turbine

_{p}-λ” curves of both stand-alone turbine and twin rotors respectively, and each turbine has the same size. C

_{p}can be obtained from Equation (10). The results are shown as Figure 12, where S stands for the stand-alone turbine and D stands for the twin rotors. Subsequent statements follow the same naming rules. It is noticed that the results are obtained from 2D numerical simulation. The average C

_{p}is larger than the true value due to the fact that spoke effect and 3D effect were neglected in the numerical simulation. Li et al. [41] has carried out research about the influence of 3D effects and spoke effect on the hydrodynamic performance of the turbine. However, the variation tendency of the two curves has a good agreement with each other.

#### 4.3. Effect of the Relative Distance of the System

## 5. Discussion

_{p}= 16/27) for the maximum efficiency of a turbine in an infinite domain is increased by a factor of (1-A/A

_{c})

^{−2}in a channel (A is the cross-sectional area of the turbine; A

_{c}is the channel cross-sectional area). The actual power still increases as the area ratio A/A

_{c}increases (in this case, the flow domain is like a flow channel, [A/A

_{c}]

_{twin-rotors}> [A/A

_{c}]

_{single rotor}). More details about the power output increasing can be seen in [42]. Nevertheless, the distance between two main shafts should also not be too close to each other for the convenience of maintenance. The distance should be carefully considered in real deployment of the twin-rotors system. It is noticed that the maximum power output efficiency can be achieved when the ratio between the two main axis distance and turbine diameter is around 9/4. If the ratio keeps decreasing, the power output efficiency of the twin-rotors system gradually decreases. The wake flow velocity distribution change in the middle channel of the twin-rotors system is one of the main causes of power output variation of twin-rotors system.

## 6. Conclusions

- The interactions between the twin rotors changes the velocity and pressure in the rotor disk domain, thus leading to an increase of the power output in the twin-rotors system.
- The twin-rotors system has the advantages of increasing power output without having large influence on fatigue life and structure strength. The load coefficients of twin rotors are bigger than that of stand-alone turbine by less than 5%. The cyclic variation tendency of twin-rotors system is almost the same with the stand-alone turbine system.
- The optimal ratio between the two main axis distances and turbine diameter is around 9/4 for the twin-rotors system in this manuscript. The optimal ratio is not applicable to a different twin-rotors system and the actual optimal ratio for other specific twin-rotors system should be carefully considered.
- The converging tendency of the wake flow field behind the twin rotors is the main cause of decrease of the twin-rotors system when the ratio between two main axis and turbine diameter is larger than 9/4.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C_{p} | Power output efficiency |

C_{q} | Torque coefficient |

D | Turbine diameter |

b | Span of the blade |

C | Chord length of the blade |

$\omega $ | Angular velocity of the turbine |

$\theta $ | Blade position angle |

$\phi $ | Blade pitch angle |

$\alpha $ | Attack angle |

$\rho $ | Density of Water |

$\sigma $ | Compactness of the turbine |

λ | Tip speed ratio |

L | Lift force of a single blade |

Dr | Drag force of a single blade |

${f}_{n}$ | Normal force coefficient of the blade |

${f}_{t}$ | Tangential force coefficient of the blade |

${f}_{x}$ | Thrust coefficient of the blade |

${f}_{y}$ | Lateral force coefficient of the blade |

${F}_{x}$ | Thrust of the rotor |

${F}_{y}$ | Lateral force of the rotor |

${C}_{t}$ | Tangential force coefficient of the blade |

${C}_{n}$ | Normal force coefficient of the blade |

${C}_{Fx}$ | Thrust coefficient |

${C}_{Fy}$ | Lateral force coefficient |

${C}_{Q}$ | Torque coefficient |

N-S | Navier–Stokes |

RMS | Root mean square |

FVM | Finite volume method |

Y plus | Dimensionless parameter of determining the scale of the first layer |

CFD | Computational fluid dynamics |

CEL | CFX expression language |

DIST | Dimensionless parameter: ratio between two main axis distance and turbine diameter |

DVM-UBC | Discrete vortex method–University of British Columbia |

SST | Shear stress transport |

RANS | Reynolds average Naiver–Stokes |

ICEM | Integrated Computer Engineering and Manufacturing |

Dw | Distance between the wall and center of the turbine |

## References

- Bahaj, A.B.S. Generating electricity from the oceans. Renew. Sustainable Energy Rev.
**2011**, 15, 3399–3416. [Google Scholar] [CrossRef] - Melo, A.B.; Sweeney, E.; Villate, J.L. Global review of recent ocean energy activities. Mar. Technol. Soc. J.
**2013**, 47, 97–103. [Google Scholar] [CrossRef] - Nachtane, M.; Tarfaoui, M.; Saifaoui, D.; Hilmi, K.; Moumen, A.E. Assessment of energy production potential from tidal stream currents in Morocco. Energies
**2018**, 11, 1065. [Google Scholar] [CrossRef] - Jo, C.H.; Kim, D.Y.; Hwang, S.J.; Goo, C.H. Shape design of the duct for tidal converters using both numerical and experimental approaches (pre-2015). Energies
**2016**, 9, 185. [Google Scholar] [CrossRef] - Li, D.; Wang, S.; Yuan, P. An overview of development of tidal current in China: Energy resource, conversion technology and opportunities. Renew. Sustainable Energy Rev.
**2010**, 14, 2896–2905. [Google Scholar] [CrossRef] - Zhang, L.; Li, X.; Geng, J.; Zhang, X. Tidal current energy update 2013. Adv. New Renew. Energy
**2013**, 1, 53–68. [Google Scholar] - Khan, M.J.; Bhuyan, G.; Iqbal, M.T.; Quaicoe, J.E. Hydrokinetic energy conversion systems and assessment of horizontal and vertical axis turbines for river and tidal applications: A technology status review. Appl. Energy
**2009**, 86, 1823–1835. [Google Scholar] [CrossRef] - Li, Y. Ocean Energy Development; Ocean Publishers: Beijing, China, 2008; pp. 101–138. [Google Scholar]
- Wang, S. Study on Hydrodynamic Performances of a Tidal Current Energy Conversion Device with Flexible Blade Turbine. Ph.D. Thesis, Ocean University of China, Qingdao, China, 2009. [Google Scholar]
- Chen, F. Kuroshio power plant development plan. Renew. Sustainable Energy Rev.
**2010**, 14, 2655–2668. [Google Scholar] [CrossRef] - Porter, K.; Ordonez-Sanchez, S.; Johnstone, C.; Conesa, S. Integration of a direct drive contra-rotating generator with point absorber wave energy converters. In Proceedings of the 12th European Wave and Tidal Energy Conference, Cork, Ireland, 27 August–1 September 2017. [Google Scholar]
- Ma, Y.; Li, B.; Xu, Y.; Dong, Y. Design and hydrodynamic characteristics of the gate-type tidal current energy converter. In Proceedings of the 26th International Ocean and Polar Engineering Conference, Rhodes, Greece, 26 June–1 July 2016. [Google Scholar]
- Ma, Y.; Li, T.F.; Zhang, L.; Sheng, Q.H.; Zhang, X.W.; Jiang, J. Experimental study on hydrodynamic characteristics of vertical-axis floating tidal current energy power generation device. Chin. Ocean Eng.
**2016**, 30, 749–762. [Google Scholar] [CrossRef] - Myers, L.E.; Bahaj, A.S. An experimental investigation simulating flow effects in first generation marine current energy converter arrays. Renew. Energy
**2012**, 37, 28–36. [Google Scholar] [CrossRef] [Green Version] - Sutherland, D.; Ordonez-Sanchez, S.; Belmont, M.R.; Moon, I.; Steynor, J.; Davey, T.; Bruce, T. Experimental optimisation of power for large arrays of cross-flow tidal turbines. Renew. Energy
**2018**, 116, 685–696. [Google Scholar] [CrossRef] - Bai, G.; Li, J.; Fan, P.; Li, G. Numerical investigations of the effects of different arrays on power extractions of horizontal axis tidal current turbines. Renew. Energy
**2013**, 53, 180–186. [Google Scholar] [CrossRef] - Li, Y.; Calışal, S.M. Modeling of twin-rotors systems with vertical axis tidal current turbines: Part I—Power output. Ocean Eng.
**2010**, 37, 627–637. [Google Scholar] [CrossRef] - Li, Y.; Calisal, S.M. Modeling of twin-rotors systems with vertical axis tidal current turbine: Part II—Torque fluctuation. Ocean Eng.
**2011**, 38, 550–558. [Google Scholar] [CrossRef] - Goude, A.; Ågren, O. Numerical simulation of a farm of vertical axis marine current turbines. In Proceedings of the 29th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, Shanghai, China, 6–10 June 2010; pp. 335–344. [Google Scholar]
- Dyachuk, E.; Goude, A.; Lalander, E.; Bernhoff, H. Influence of incoming flow direction on spacing between vertical axis marine current turbines placed in a row. In Proceedings of the 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, Rio de Janeiro, Brazil, 1–6 July 2012; pp. 285–291. [Google Scholar]
- Gebreslassie, M.G.; Tabor, G.; Belmont, M.R. CFD simulations for sensitivity analysis of different parameters to the wake characteristics of tidal turbine. Open J. Fluid Dyn.
**2012**, 2, 56–64. [Google Scholar] [CrossRef] - Nishino, T.; Willden, R.H.J. The efficiency of an array of tidal turbines partially blocking a wide channel. J. Fluid Mech.
**2012**, 708, 596–606. [Google Scholar] [CrossRef] - Georgescu, A.M.; Georgescu, S.C.; Cosoiu, C.I.; Alboiu, N.; Hamzu, A. Velocity field in the wake of a hydropower farm equipped with Achard turbines. IOP Conf. Ser. Earth Environ. Sci.
**2010**, 12, 012108. [Google Scholar] [CrossRef] [Green Version] - Ansys Inc. ANSYS Fluent; ANSYS Inc.: Pittsburgh, PA, USA, 2015. [Google Scholar]
- Wang, K.; Su, K.; Zhang, L. Impact of phase angle on the hydrodynamic performance of a bi-unit vertical axis tidal current energy. J. Harbin Eng. Univ.
**2016**, 37, 104–109. [Google Scholar] - Ansys Inc. ANSYS CFX; ANSYS Inc.: Pittsburgh, PA, USA, 2015. [Google Scholar]
- Ansys Inc. ANSYS CFX User Manual; ANSYS Inc.: Pittsburgh, PA, USA, 2015. [Google Scholar]
- Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J.
**1994**, 32, 1598–1605. [Google Scholar] [CrossRef] [Green Version] - Holst, M.A.; Dahlhaug, O.G.; Faudot, C. Cfd analysis of wave-induced loads on tidal turbine blades. IEEE J. Oceanic Eng.
**2015**, 40, 506–521. [Google Scholar] [CrossRef] - Menter, F.R.; Langtry, R.; Völker, S. Transition modelling for general purpose CFD codes. Flow Turbul. Combust.
**2006**, 77, 277–303. [Google Scholar] [CrossRef] - Ponta, F.; Dutt, G. An improved vertical-axis water-current turbine incorporating a channelling device. Renew. Energy.
**2000**, 20, 223–241. [Google Scholar] [CrossRef] - Shiono, M.; Suzuki, K.; Kiho, S. Output characteristics of Darrieus water turbine with helical blades for Tidal Current generations. In Proceedings of the 12th International Offshore and Polar Engineering Conference, Kitakyushu, Japan, 26–31 May 2002. [Google Scholar]
- Yang, C.; Mao, Z.S. Numerical simulation of interphase mass transfer with the level set approach. Chem. Eng. Sci.
**2005**, 60, 2643–2660. [Google Scholar] [CrossRef] - Nejat, A.; Ollivier-Gooch, C. A high-order accurate unstructured finite volume Newton–Krylov algorithm for inviscid compressible flows. J. Comput. Phy.
**2008**, 227, 2582–2609. [Google Scholar] [CrossRef] - Tan, X.; Zhang, X. A simple O-type mesh generation method. J. Changsha Univ. Electr. Power
**2001**, 4, 40–53. [Google Scholar] - Maganga, F.; Germain, G.; King, J.; Pinon, G.; Rivoalen, E. Experimental characterisation of flow effects on marine current turbine behaviour and on its wake properties. IET Renew. Power Gener.
**2010**, 4, 498–509. [Google Scholar] [CrossRef] - ANSYS Inc. ANSYS CFX Modeling Guide. Release 13.0; ANSYS Inc.: Pittsburgh, PA, USA, 2010. [Google Scholar]
- Gosselin, R. Analysis and Optimization of Vertical Axis Turbines. Ph.D. Thesis, Université Laval, Quebec, QC, Canada, 2015. [Google Scholar]
- Tralli, A.; Bijlsma, A.C.; te Velde, W.; de Haas, P. CFD study on free-surface influence on tidal turbines in hydraulic structures. In Proceedings of the ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering, St. John’s, NL, Canada, 31 May–5 June 2015. [Google Scholar]
- Strickland, J.H.; Webster, B.T.; Nguyen, T. A vortex model of the Darrieus turbine: An analytical and Experimental Study. J. Fluids Eng.
**1979**, 101, 500–505. [Google Scholar] [CrossRef] - Li, Y.; Calisal, S.M. Three-dimensional effects and arm effects on modeling a vertical axis tidal current turbine. Renew. Energy
**2010**, 35, 2325–2334. [Google Scholar] [CrossRef] - Garrett, C.; Cummins, P. The efficiency of a turbine in a tidal channel. J. Fluid Mech.
**2007**, 588, 243–251. [Google Scholar] [CrossRef]

**Figure 4.**Mesh configuration, (

**a**) mesh in blade domain, (

**b**) mesh in rotating domain, (

**c**) mesh in outer domain, (

**d**) effect picture of twin-rotors system.

**Figure 6.**Variation trend of torque coefficient of single turbine with phase angle for three different meshes.

**Figure 7.**Variation trend of torque coefficient of single turbine with phase angle for three different timesteps

**Figure 8.**Variation trend of torque coefficient of single turbine with phase angle and varying D

_{w}for slip wall.

**Figure 9.**Variation trend of torque coefficient of single turbine with phase angle and varying D

_{w}for non-slip wall.

**Figure 10.**Comparison of normal force coefficient between numerical simulation results and experimental results in the literature.

**Figure 11.**Comparison of tangential force coefficient between numerical simulation results and experimental results in the literature.

**Figure 12.**Comparison of power output efficient with different lambda between stand-alone turbine and twin-rotors turbine.

**Figure 13.**Tangential and normal force coefficient curves, (

**a**) normal force coefficient curves of stand-alone turbine and twin-rotors system, (

**b**) tangential force coefficient curves of stand-alone turbine and twin-rotors turbine.

**Figure 14.**Lateral force, thrust and torque coefficient curve, (

**a**) thrust coefficient curves of stand-alone turbine and twin-rotors system, (

**b**) lateral force coefficient curves of stand-alone turbine and twin-rotors system, (

**c**) torque coefficient curves of stand-alone turbine and twin-rotors system.

**Figure 15.**Cloud picture of velocity in the stand-alone turbine and twin-rotors turbine flow field. (

**a**) Contour of velocity in the stand-alone turbine flow field, (

**b**) contour of velocity of one of the rotors for the twin-rotors turbine flow field.

**Figure 16.**Cloud picture of pressure in the stand-alone turbine and twin-rotors turbine flow field. (

**a**) Contour of pressure in the stand-alone turbine flow field, (

**b**) contour of pressure in the twin-rotors turbine flow field.

**Figure 17.**Power output efficient of twin-rotors system at different tip speed ratio and different axis distances.

**Figure 18.**Cloud picture of velocity in twin-rotors system field with various axis distances. (

**a**) Relative distance DIST = 11/4, (

**b**) Relative distance DIST = 9/4, (

**c**) Relative distance DIST = 7/4.

Mesh | Total Mesh Quantity (×10^{3}) | Y Plus | Simulation Time (h) | Number of Mesh Layer | Thickness of the First Layer (×10^{−4} m) |
---|---|---|---|---|---|

1 | 45 | 21.5–38.2 | 4 | 30 | 4 |

2 | 119 | 2.65–4.76 | 12 | 30 | 1 |

3 | 274 | 0.83–1.96 | 26 | 30 | 0.5 |

DIST | Relative Increase of C_{p}/% | ||||
---|---|---|---|---|---|

Lambda = 1.0 | Lambda = 1.5 | Lambda = 2.0 | Lambda = 2.5 | Lambda = 3.0 | |

12/4 | 0.65 | 8.74 | 13.39 | 15.73 | 21.24 |

11/4 | 0.74 | 10.55 | 14.63 | 16.63 | 22.63 |

10/4 | 0.42 | 11.57 | 14.99 | 16.45 | 19.55 |

9/4 | 0.23 | 12.76 | 14.03 | 12.01 | 8.57 |

8/4 | 0.38 | 12.37 | 10.99 | 10.04 | 5.53 |

7/4 | 0.13 | 11.71 | 8.90 | 7.89 | 9.07 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ma, Y.; Hu, C.; Li, Y.; Li, L.; Deng, R.; Jiang, D.
Hydrodynamic Performance Analysis of the Vertical Axis Twin-Rotor Tidal Current Turbine. *Water* **2018**, *10*, 1694.
https://doi.org/10.3390/w10111694

**AMA Style**

Ma Y, Hu C, Li Y, Li L, Deng R, Jiang D.
Hydrodynamic Performance Analysis of the Vertical Axis Twin-Rotor Tidal Current Turbine. *Water*. 2018; 10(11):1694.
https://doi.org/10.3390/w10111694

**Chicago/Turabian Style**

Ma, Yong, Chao Hu, Yulong Li, Lei Li, Rui Deng, and Dapeng Jiang.
2018. "Hydrodynamic Performance Analysis of the Vertical Axis Twin-Rotor Tidal Current Turbine" *Water* 10, no. 11: 1694.
https://doi.org/10.3390/w10111694