# A New Wind Turbine CFD Modeling Method Based on a Porous Disk Approach for Practical Wind Farm Design

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## Abstract

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_{RC}was estimated by comparison with the time-averaged wind speed database in the wind turbine wake region with fully resolved geometries, combined with unsteady Reynolds-averaged Navier–Stokes (RANS) equations, implemented using the ANSYS(R) CFX(R) software. Here, product names (mentioned herein) may be trademarks of their respective companies. As a result, in the range from x = 5D of the near wake region to x = 10D of the far wake region, by selecting model parameter C

_{RC}, it was clarified that it is possible to accurately evaluate the time-averaged wind speed deficits at those separation distances. We also examined the effect of the spatial grid resolution using the CFD PD wake model that is proposed in the present study, clarifying that the spatial grid resolution has little effect on the simulation results shown here.

## 1. Introduction

## 2. Wind Tunnel Experiment Using a 1/88 Wind Turbine Scale Model and Fully Resolved Geometries Combined with Unsteady RANS by ANSYS(R) CFX(R)

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## 3. Fully Resolved Geometries Combined with Unsteady RANS, Calculated by ANSYS(R) CFX(R) for a Real Wind Turbine

^{+}= 2.3 based on the numerical results in described in Chapter 2. The inflow wind speed distribution followed the power law velocity profile, where N = 10, and the wind speed at the hub center of the wind turbine was 10 m/s. Here, the wind speed of 10 m/s corresponds to the vicinity of the maximum value of the power coefficient Cp. The k-ω SST model (unsteady RANS) was adopted as the turbulence model, the same as in the simulation in Chapter 2. The other simulation conditions were as shown in Table 2.

## 4. Large-Eddy Simulation Using the Porous Disk Model Approach for Real Wind Turbines

_{RC}(the drag coefficient) instead of the thrust coefficient Ct. Furthermore, the spatial distribution was given in the swept area by multiplying the model parameter C

_{RC}by the cosine-shaped distribution function shown in Figure 16. In the swept area, the model parameter C

_{RC}, as a resistance value, reaches a maximum at the hub center of the wind turbine, and its value becomes the minimum (zero) toward the tip of the wind turbine blade. In order to verify the validity of the CFD PD wake model proposed in the present study and to determine the optimal value of the model parameter C

_{RC}, a comparison was made with the fully resolved geometries combined with unsteady RANS approach by ANSYS(R) CFX(R), described in Chapter 3.

_{RC}of the CFD PD wake model set in the swept area of wind turbine. Based on this assumption, the spatial distribution in the swept area of the wind turbine was determined by multiplying the parameter C

_{RC}by the correction function such as cosine-shaped distribution function. That is, the C

_{RC}is not set to a constant value in the swept area of the wind turbine. The spatial distribution of C

_{RC}is gradually changed from the center of the wind turbine to the tip using a correction function. This is based on the physical consideration of the flow characteristics in the wind turbine wake region (results of the wind tunnel experiment conducted in this study and past research results [17]). This is also a novel idea in this research that has never existed before. Furthermore, the correction function is not limited to the cosine-shaped distribution function (see Appendix A). For example, by using a Gaussian function or a spline function to modify the model parameter C

_{RC}distribution of the CFD PD wake model in the swept area of wind turbine more precisely, the amount of wind velocity (U-velocity) loss in the streamwise direction can be further improved. In the future, we plan to further study how to give the spatial distribution of C

_{RC}for a wide range of wind speed classes and different wind turbine sizes including large offshore wind turbines of 10 MW or higher power levels.

_{RC}, which is the only model parameter in the CFD PD wake model, was determined by conducting a parameter survey so that the wake error defined in Equation (1) was minimized. For the target wind speed shown in Equation (1), the huge computation results of the fully resolved geometries combined with unsteady RANS by ANSYS(R) CFX(R), described in Chapter 3 (time-averaged wind speed database in the wind turbine wake region), were used.

_{RC}, is the resistance coefficient, and we used 5, 6, 7, 8, 9, and 10 for it (C

_{RC}). The RANS results and the present LES results were compared in the latest findings [26], and the prediction accuracy of the present LES approach by comparison with wind tunnel experiments was discussed [27].

^{–4}D/U

_{in}, where D represents the rotor diameter.

_{RC}= 5.0 to 10.0) from the newly proposed method in the present study. In other words, in the range of x = 5D of the near wake region to x = 10D of the far wake region, this suggests that wind energy/wind farm developers can accurately evaluate the average velocity deficit at the separation distance by selecting the model parameter C

_{RC}corresponding to the required separation distance. For example, if wind energy/wind farm developers want to know the exact time-averaged velocity deficit at x = 5D, they should set C

_{RC}to 9.0 or 10.0, or if they want to know the exact time-averaged velocity deficit at x = 10D, they should set C

_{RC}to 5.0.

_{RC}= 9.0 or 10.0 of the CFD PD wake model has the smallest error from the numerical result determined by ANSYS(R) CFX(R). At x = 5D in the near wake region, it is considered that the separated flows from the wind turbine nacelle and tower strongly influence the formation of the wake region behind the wind turbine. On the other hand, at x = 10D (far wake region) downstream of the wind turbine, the result of the model parameter C

_{RC}= 5.0 of the CFD PD wake model has the smallest error from the numerical result determined by ANSYS(R) CFX(R). As mentioned above, these results confirm that wind energy/wind farm developers can accurately predict the time-averaged velocity deficit at the separation distance by selecting an appropriate value for the model parameter C

_{RC}. In addition, further examination on the spatial distribution of model parameter C

_{RC}set in the swept area of the wind turbine is required for a wide range of wind speed classes and different wind turbine sizes including large offshore wind turbines of 10 MW or higher power levels.

## 5. Conclusions

_{RC}was estimated by comparing the time-averaged wind speed database in the wind turbine wake region by the previously described fully resolved geometries combined with unsteady RANS found by ANSYS(R) CFX(R). As a result, in the range from x = 5D of the near wake region to x = 10D of the far wake region, by selecting model parameter C

_{RC}corresponding to the separation distance that wind energy/wind farm developers pay attention to, it was clarified that it is possible to accurately evaluate the time-averaged wind speed deficits at a given separation distance. For example, if wind energy/wind farm developers want to know the exact time-averaged velocity deficit at x = 5D, they should set C

_{RC}to 9.0 or 10.0, or if they want to know the exact time-averaged velocity deficit at x = 10D, they should set C

_{RC}to 5.0. We also examined the effect of the spatial grid resolution using the CFD PD wake model proposed in the present study and clarified that the spatial grid resolution has little effect on simulation results shown here.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Examination of Various Correction Functions in the CFD PD Wake Model Proposed in the Present Study

_{RC}(the drag coefficient) instead of the thrust coefficient Ct. Furthermore, the spatial distribution was given in the swept area by multiplying the model parameter C

_{RC}by the cosine-shaped distribution function. In the swept area, the model parameter C

_{RC}, as a resistance value, reaches a maximum at the hub center of the wind turbine, and its value becomes the minimum (zero) toward the tip of the wind turbine blade. In the first place, it is difficult to theoretically express the wind velocity distribution in the complicated wake flows as a function. However, we would like to emphasize that we have found that it can be expressed approximately by a simple cosine-shaped function based on the physical consideration of the flow characteristics in the wind turbine wake region [17]. Of course, the correction function is not limited to the cosine-shaped function. Here, the examination results of a total of four patterns, including the cosine-shaped function, are shown (see Figure A1). The bell-shaped function shown in Figure A1 is described by the following formula:

**Figure A1.**Four types of function shapes examined in this study. (

**a**) constant; (

**b**) cosine-shaped function; (

**c**) bell-shaped function; (

**d**) cosine-shaped + bell-shaped function.

_{RC}for a wide range of wind speed classes and different wind turbine sizes including large offshore wind turbines of 10 MW or higher power levels.

## Appendix B. Mutual Interference of Wind Turbine Wakes Formed from Multiple Wind Turbines by the CFD PD Wake Model Proposed in the Present Study

_{RC}was equal to 5 in the CFD PD wake model. It can be clearly seen that a wind turbine wake is formed downstream from each wind turbine. It can be observed that the wind turbine wakes formed downstream of each wind turbine strongly interfere with each other at sea. From the above, in a situation where multiple wind turbines are installed, it has been visually confirmed that the mutual interference of wind turbine wakes can be reproduced using the CFD PD wake model.

Wind Turbine Number | Capacity (MW) | Hub Height (m) | Rotor Diameter (m) |
---|---|---|---|

1 | 1.5 | 65 | 70 |

2 | |||

3 | |||

4 | |||

5 | |||

6 | |||

7 | |||

8 | |||

9 | |||

10 | |||

11 | 3.3 | 84 | 112 |

12 | |||

13 | 2.0 | 65 | 86 |

14 | |||

15 | 1.99 | 67 | 80 |

16 | 2.7 | 80 | 103 |

17 | 5.0 | 89.4 | 136 |

18 | 2.0 | 80 | 83 |

**Figure A3.**LES using the CFD PD wake model for multiple wind turbines. The blue area indicates the sea.

**Figure A4.**Instantaneous U-velocity spatial distribution at 90 m above ground level and at the outflow boundary using the CFD PD wake model (C

_{RC}= 5.0), considering an instantaneous field.

## References

- Crespo, A.; Hernández, J.; Frandsen, S. Survey of modelling methods for wind turbine wakes and wind farms. Wind Energy
**1999**, 2, 1–24. [Google Scholar] [CrossRef] - Hansen, M.O.; Sørensen, J.N.; Voutsinas, S.; Sørensen, N.; Madsen, H.A. State of the art in wind turbine aerodynamics and aeroelasticity. Prog. Aerosp. Sci.
**2006**, 42, 285–330. [Google Scholar] [CrossRef] - Zhang, P.; Huang, S. Review of aeroelasticity for wind turbine: Current status, research focus and future perspectives. Front. Energy
**2011**, 5, 419–434. [Google Scholar] [CrossRef] - Sanderse, B.; van der Pijl, S.; Koren, B. Review of computational fluid dynamics for wind turbine wake aerodynamics. Wind Energy
**2011**, 14, 799–819. [Google Scholar] [CrossRef] [Green Version] - Hewitt, S.; Margetts, L.; Revell, A. Building a Digital Wind Farm. Arch. Comput. Methods Eng.
**2018**, 25, 879–899. [Google Scholar] [CrossRef] [Green Version] - Porté-Agel, F.; Bastankhah, M.; Shamsoddin, S. Wind-Turbine and Wind-Farm Flows: A Review. Bound.-Layer Meteorol.
**2020**, 174, 1–59. [Google Scholar] [CrossRef] [Green Version] - Rodrigues, R.V.; Lengsfeld, C. Development of a Computational System to Improve Wind Farm Layout, Part II: Wind Turbine Wakes Interaction. Energies
**2019**, 12, 1328. [Google Scholar] [CrossRef] [Green Version] - Available online: https://www.ansys.com/products/fluids/ansys-cfx (accessed on 1 March 2020).
- Available online: https://www.plm.automation.siemens.com/global/de/products/simcenter/STAR-CCM.html (accessed on 1 March 2020).
- Stevens, R.J.; Martínez-Tossas, L.A.; Meneveau, C. Comparison of wind farm large eddy simulations using actuator disk and actuator line models with wind tunnel experiments. Renew. Energy
**2018**, 116, 470. [Google Scholar] [CrossRef] - Lin, M.; Porté-Agel, F. Large-Eddy Simulation of Yawed Wind-Turbine Wakes: Comparisons with Wind Tunnel Measurements and Analytical Wake Models. Energies
**2019**, 12, 4574. [Google Scholar] [CrossRef] [Green Version] - Shen, W.Z.; Zhang, J.H.; Sørensen, J.N. The Actuator Surface Model: A New Navier—Stokes Based Model for Rotor Computations. J. Sol. Energy Eng.
**2009**, 131, 011002. [Google Scholar] [CrossRef] - Jensen, N.O. A Note on Wind Generator Interaction; Technical Report Risoe-M-2411(EN); Risø National Laboratory: Roskilde, Denmark, 1983. [Google Scholar]
- Katic, I.; Højstrup, J.; Jensen, N.O. A Simple Model for Cluster Efficiency. In Proceedings of the European Wind Energy Association Conference & Exhibition (EWEC’86), Italy, Rome, 6–8 October 1986; Volume 1, pp. 407–410. [Google Scholar]
- Shaw, R.H.; Schumann, U. Large-eddy simulation of turbulent flow above and within a forest. Bound.-Layer Meteorol.
**1992**, 61, 47–64. [Google Scholar] [CrossRef] [Green Version] - Uchida, T. Numerical Investigation of Terrain-Induced Turbulence in Complex Terrain Using High-Resolution Elevation Data and Surface Roughness Data Constructed with a Drone. Energies
**2019**, 12, 3766. [Google Scholar] [CrossRef] [Green Version] - Uchida, T.; Ohya, Y.; Sugitani, K. Comparisons between the wake of a wind turbine generator operated at optimal tip speed ratio and the wake of a stationary disk. Model. Simul. Eng.
**2011**, 2011, 749421. [Google Scholar] [CrossRef] [Green Version] - Wagner, R.; Cañadillas, B.; Clifton, A.; Feeney, S.; Nygaard, N.; Poodt, M.; St Martin, C.; Tüxen, E.; Wagenaar, J.W. Rotor equivalent wind speed for power curve measurement—Comparative exercise for IEA Wind Annex 32. In Journal of Physics: Conference Series; IOP Publishing: Bristol, UK, 2014; Available online: https://iopscience.iop.org/article/10.1088/1742-6596/524/1/012108 (accessed on 1 March 2020).
- Uchida, T.; Araya, R. Practical Applications of the Large-Eddy Simulation Technique for Wind Environment Assessment around New National Stadium, Japan (Tokyo Olympic Stadium). Open J. Fluid Dyn.
**2019**, 9, 269. [Google Scholar] [CrossRef] [Green Version] - Uchida, T.; Kawashima, Y. New Assessment Scales for Evaluating the Degree of Risk of Wind Turbine Blade Damage Caused by Terrain-Induced Turbulence. Energies
**2019**, 12, 2624. [Google Scholar] [CrossRef] [Green Version] - Uchida, T.; Takakuwa, S. A Large-Eddy Simulation-Based Assessment of the Risk of Wind Turbine Failures Due to Terrain-Induced Turbulence over a Wind Farm in Complex Terrain. Energies
**2019**, 12, 1925. [Google Scholar] [CrossRef] [Green Version] - Kim, J.; Moin, P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys.
**1985**, 59, 308. [Google Scholar] [CrossRef] - Kajishima, T. Upstream-shifted interpolation method for numerical simulation of incompressible flows. Bull. Jpn. Soc. Mech. Eng. B
**1994**, 60, 3319. [Google Scholar] [CrossRef] - Kawamura, T.; Takami, H.; Kuwahara, K. Computation of high Reynolds number flow around a circular cylinder with surface roughness. Fluid Dyn. Res.
**1986**, 1, 145–162. [Google Scholar] [CrossRef] - Inagaki, M.; Kondoh, T.; Nagano, Y. A Mixed-Time-Scale SGS Model with Fixed Model-Parameters for Practical LES. ASME. J. Fluids Eng.
**2005**, 127, 1–13. [Google Scholar] [CrossRef] - Uchida, T.; Li, G. Comparison of RANS and LES in the Prediction of Airflow Field over Steep Complex Terrain. Open J. Fluid Dyn.
**2018**, 8, 286. [Google Scholar] [CrossRef] [Green Version] - Uchida, T.; Ohya, Y. Micro-siting Technique for Wind Turbine Generators by Using Large-Eddy Simulation. J. Wind Eng. Ind. Aerodyn.
**2008**, 96, 2121. [Google Scholar] [CrossRef] - Wu, Y.-T.; Porté-Agel, F. Atmospheric Turbulence Effects on Wind-Turbine Wakes: An LES Study. Energies
**2012**, 5, 5340–5362. [Google Scholar] [CrossRef] - Desmond, C.; Murphy, J.; Blonk, L.; Haans, W. Description of an 8 MW reference wind turbine. Journal of Physics: Conference Series. In Journal of Physics: Conference Series; IOP Publishing: Bristol, UK, 2016; Volume 753, p. 092013. [Google Scholar]

**Figure 4.**The 1/88 wind turbine scale model used in the present study. (

**a**) Front view; (

**b**) rear view.

**Figure 5.**Relationship between the tip speed ratio (TSR; horizontal axis) and the power coefficient Cp. (vertical axis) of the 1/88 scale wind turbine model obtained in the wind tunnel experiment.

**Figure 6.**Computational domain and computational grid simulation of a wind tunnel experiment using a 1/88 scale wind turbine model, using the fully resolved geometries combined with large-eddy simulation (LES) simulations approach, produced by ANSYS(R) CFX(R).

**Figure 7.**Computational grid for 1/88 scale wind turbine model (1/3 is cut out, but this was actually simulated at 360 deg). (

**a**) Total model; (

**b**) rotating part; (

**c**) wind turbine blade.

**Figure 8.**Comparison of grid resolution near blade tip. (

**a**) Coarse grid; (

**b**) standard (medium) grid; (

**c**) fine grid.

**Figure 9.**Simulation results for the 1/88 scale wind turbine model, the spatial distribution of instantaneous U-velocities, the standard grid, and the fully resolved geometries combined with unsteady RANS results produced by ANSYS(R) CFX(R). (

**a**) x–z plane; (

**b**) y–z plane.

**Figure 10.**Comparison of time-averaged U-velocities in the measurement line (x = 0.5D). indicated by the dotted line in Figure 9a.

**Figure 11.**Image diagram of the wake error rate related to the time-averaged wind speed distribution in the wind turbine wake region.

**Figure 12.**Comparison of wake error rate of time-averaged U-velocity in measurement line (x = 0.5D) shown by dotted line in Figure 9a.

**Figure 13.**Comparison of the change in time of the instantaneous U-velocity at the measurement point (x = 0.5D, y = −0.5D) indicated by the black circle symbol in Figure 9a.

**Figure 14.**Computational domain and computational grid for a real wind turbine, using the fully resolved geometries combined with the unsteady RANS approach using ANSYS(R) CFX(R).

**Figure 15.**Simulation results for the real wind turbine and the spatial distribution of instantaneous U-velocity found by the fully resolved geometries combined with unsteady RANS approach by ANSYS(R) CFX(R) CFX. (

**a**) Side view; (

**b**) front view, x = 5D (near wake region); (

**c**) font view, x = 10D (far wake region).

**Figure 16.**Image of the computational fluid dynamics (CFD) porous disk (PD) wake model proposed. in the present study.

**Figure 17.**Computational domain and computational grid in the case of LES.using the CFD PD wake model.

**Figure 18.**Simulation results of time-averaged field for a real wind turbine (C

_{RC}= 10.0), spatial distribution of time-averaged U-velocities, and LES using the CFD PD wake model. (

**a**) Side view; (

**b**) rear view, x = 5D (near wake region); (

**c**) rear view, x = 10D (far wake region).

**Figure 19.**Comparison of time-averaged U-velocity space distribution at the center of the wind turbine hub with simulation results of time-averaged field for a real wind turbine.

**Figure 20.**Comparison of vertical distribution of time-averaged U-velocities. (

**a**) x = 5D (near wake region); (

**b**) x = 10D (far wake region). Simulation results of a time-averaged field for a real wind turbine shown here.

**Figure 21.**Wake error rate of simulation results of the CFD PD wake model with respect to the simulation results by ANSYS(R) CFX(R) in the case of a real wind turbine. (

**a**) x = 5D (near wake region); (

**b**) x = 10D (far wake region). The comparison of wake error rates was evaluated based on the simulation results shown in Figure 21.

**Figure 23.**Comparison of time-averaged U-velocity distribution at the hub center of the wind turbine using the CFD PD wake model (C

_{RC}= 10.0).

**Figure 24.**Comparison of the vertical distribution of time-averaged U-velocity using the CFD PD wake model (C

_{RC}= 10.0). (

**a**) x = 5D (near wake region); (

**b**) x = 10D (far wake region).

**Table 1.**Simulation conditions for the 1/88 scale wind turbine model. RANS: Reynolds-averaged Navier–Stokes.

Pre-Processing (Geometry/Mesh Generation) | ANSYS(R) ICEM CFD(TM) v14.5 |

Solver | ANSYS(R) CFX(R) v19.3 |

Turbulence Model | Unsteady RANS (SST k-ω) |

Convective Difference Scheme | High Resolution |

Number of Meshes | Approximately 15 Million |

Time Increment (sec) | 1.96e-3 (5 deg/1 step) |

Analysis Time (day) | 3 (40 Blade Rotations) |

Sampling Time (sec) | 4.23 |

Number of Blade Rotations during Sampling | 30 |

Computer Environment | Number of Cores: Total of 1440 cores (60 nodes) Single-node Performance: 24 cores/1 node, Intel Xeon Gold 6136 (3.0 GHz) |

Pre-Processing (Geometry/Mesh Generation) | ANSYS(R) ICEM CFD(TM) v14.5 |

Solver | ANSYS(R) CFX(R) v19.3 |

Turbulence Model | Unsteady RANS (SST k-ω) |

Convective Difference Scheme | High Resolution |

Number of Meshes | Approximately 14 Million |

Time Increment (sec) | 5.45e-2 (5 deg/1 step) |

Analysis Time (day) | 10 (140 Blade Rotations) |

Sampling Time (sec) | 117.65 |

Number of Blade Rotations during Sampling | 30 |

Computer Environment | Number of Cores: Total of 1440 cores (60 nodes) Single-node Performance: 24 cores/1 node, Intel Xeon Gold 6136 (3.0 GHz) |

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## Share and Cite

**MDPI and ACS Style**

Uchida, T.; Taniyama, Y.; Fukatani, Y.; Nakano, M.; Bai, Z.; Yoshida, T.; Inui, M.
A New Wind Turbine CFD Modeling Method Based on a Porous Disk Approach for Practical Wind Farm Design. *Energies* **2020**, *13*, 3197.
https://doi.org/10.3390/en13123197

**AMA Style**

Uchida T, Taniyama Y, Fukatani Y, Nakano M, Bai Z, Yoshida T, Inui M.
A New Wind Turbine CFD Modeling Method Based on a Porous Disk Approach for Practical Wind Farm Design. *Energies*. 2020; 13(12):3197.
https://doi.org/10.3390/en13123197

**Chicago/Turabian Style**

Uchida, Takanori, Yoshihiro Taniyama, Yuki Fukatani, Michiko Nakano, Zhiren Bai, Tadasuke Yoshida, and Masaki Inui.
2020. "A New Wind Turbine CFD Modeling Method Based on a Porous Disk Approach for Practical Wind Farm Design" *Energies* 13, no. 12: 3197.
https://doi.org/10.3390/en13123197