# Comparison of Blade Element Method and CFD Simulations of a 10 MW Wind Turbine

## Abstract

**:**

## 1. Motivation and State of the Art

## 2. Simulation Approaches

#### 2.1. Blade Element and Momentum

#### 2.1.1. One Dimensional Momentum Theory and the Momentum Transfer

#### 2.1.2. Blade Element Theory

#### 2.1.3. B-GO Code Description

`read_data`,

`variable_assignment`,

`data_preparation`,

`interpolate_polar`,

`interpolate_radial`,

`extrapolation`,

`induction_calculation`and

`tip_loss_correction`, illustrated in Figure 3. By writing each main part of the code as a subroutine, the code can be further developed in the future by simply modifying only the respective functions.

#### 2.2. Computational Fluid Dynamics

## 3. Results and Discussion

#### 3.1. 3D CFD and BEM Comparison

#### 3.2. Simulations at Various Operating Conditions

## 4. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Bangga, G.; Hutomo, G.; Syawitri, T.; Kusumadewi, T.; Oktavia, W.; Sabila, A.; Setiadi, H.; Faisal, M.; Hendranata, Y.; Lastomo, D.; et al. Enhancing BEM simulations of a stalled wind turbine using a 3D correction model. J. Phys. Conf. Ser.
**2018**, 974, 012020. [Google Scholar] [CrossRef][Green Version] - Hutomo, G.; Bangga, G.; Sasongko, H. CFD studies of the dynamic stall characteristics on a rotating airfoil. Appl. Mech. Mater.
**2016**, 836, 109–114. [Google Scholar] [CrossRef] - Bangga, G.; Lutz, T.; Dessoky, A.; Krämer, E. Unsteady Navier-Stokes studies on loads, wake, and dynamic stall characteristics of a two-bladed vertical axis wind turbine. J. Renew. Sustain. Energy
**2017**, 9, 053303. [Google Scholar] [CrossRef][Green Version] - Betz, A. Das Maximum der theoretisch möglichen Ausnutzung des Windes durch Windmotoren. Zeitschrift Gesamte Turbinenwesten
**1920**, 20, 307–309. [Google Scholar] - Gasch, R.; Twele, J. Wind Power Plants: Fundamentals, Design, Construction and Operation; Springer Science & Business Media: Berlin, Germany, 2011. [Google Scholar]
- Glauert, H. The Elements of Aerofoil and Airscrew Theory; Cambridge University Press: Cambridge, UK, 1983. [Google Scholar]
- Ingram, G. Wind Turbine Blade Analysis Using the Blade Element Momentum Method Version 1.0; School of Engineering, Durham University: Durham, UK, 2005. [Google Scholar]
- Prandtl, L.; Betz, A. Vier Abhandlungen zur Hydrodynamik und Aerodynamik; Universitätsverlag Göttingen: Göttingen, Germany, 2010; Volume 3. [Google Scholar]
- Himmelskamp, H. Profile Investigations on a Rotating Airscrew; MAP: Göttingen, Germany, 1947. [Google Scholar]
- Sørensen, J.N. Three-Level, Viscous-Inviscid Interaction Technique for the Prediction of Separated Flow Past Rotating Wing. Ph.D. Thesis, Technical University of Denmark (DTU), Lyngby, Denmark, 1986. [Google Scholar]
- Snel, H.; Houwink, R.; Bosschers, J.; Piers, W.; Van Bussel, G.; Bruining, A. Sectional prediction of 3D effects for stalled flow on rotating blades and comparison with measurements. In Proceedings of the European Community Wind Energy Conference, HS Stevens and Associates, LÃ1, Travemuende, Germany, 8–12 March 1993; Volume 4. [Google Scholar]
- Du, Z.; Selig, M. The effect of rotation on the boundary layer of a wind turbine blade. Renew. Energy
**2000**, 20, 167–181. [Google Scholar] [CrossRef] - Bangga, G. Three-Dimensional Flow in the Root Region of Wind Turbine Rotors; Kassel University Press GmbH: Kassel, Germany, 2018. [Google Scholar]
- Bangga, G.; Kim, Y.; Lutz, T.; Weihing, P.; Krämer, E. Investigations of the inflow turbulence effect on rotational augmentation by means of CFD. J. Phys. Conf. Ser.
**2016**, 753, 022026. [Google Scholar] [CrossRef] - Bangga, G.; Lutz, T.; Jost, E.; Krämer, E. CFD studies on rotational augmentation at the inboard sections of a 10 MW wind turbine rotor. J. Renew. Sustain. Energy
**2017**, 9, 023304. [Google Scholar] [CrossRef] - Bangga, G.; Lutz, T.; Krämer, E. Root flow characteristics and 3D effects of an isolated wind turbine rotor. J. Mech. Sci. Technol.
**2017**, 31, 3839–3844. [Google Scholar] [CrossRef] - Wood, D. A three-dimensional analysis of stall-delay on a horizontal-axis wind turbine. J. Wind Eng. Ind. Aerodyn.
**1991**, 37, 1–14. [Google Scholar] [CrossRef] - Duque, E.P.; Burklund, M.D.; Johnson, W. Navier-Stokes and comprehensive analysis performance predictions of the NREL phase VI experiment. In Proceedings of the Wind Energy Symposium, Reno, NV, USA, 6–9 January 2003; pp. 43–61. [Google Scholar]
- Pape, A.L.; Lecanu, J. 3D Navier–Stokes computations of a stall-regulated wind turbine. Wind Energy Int. J. Prog. Appl. Wind Power Convers. Technol.
**2004**, 7, 309–324. [Google Scholar] [CrossRef] - Wilcox, D.C. Turbulence Modeling for CFD; DCW Industries: La Cañada Flintridge, CA, USA, 1998; Volume 2. [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] - Bangga, G.; Weihing, P.; Lutz, T.; Krämer, E. Effect of computational grid on accurate prediction of a wind turbine rotor using delayed detached-eddy simulations. J. Mech. Sci. Technol.
**2017**, 31, 2359–2364. [Google Scholar] [CrossRef] - Boorsma, K.; Schepers, J. New MEXICO experiment. Preliminary Overview with Initial Validation Technical Report ECN-E–14-048 ECN. 2014. Available online: https://www.ecn.nl/docs/library/report/2014/e14048.pdf (accessed on 16 October 2018).
- Sørensen, N.; Hansen, N.; Garcia, N.; Florentie, L.; Boorsma, K.; Gomez-Iradi, S.; Prospathopoulus, J.; Barakos, G.; Wang, Y.; Jost, E.; et al. AVATAR D2. 3–Power Curve Predictions. AVATAR Proj. 2015. Available online: http://www.eera-avatar.eu/fileadmin/mexnext/user/report-d2p3.pdf (accessed on 16 October 2018).
- Schneider, M.S.; Nitzsche, J.; Hennings, H. Accurate load prediction by BEM with airfoil data from 3D RANS simulations. J. Phys. Conf. Ser.
**2016**, 753, 082016. [Google Scholar] [CrossRef][Green Version] - Guma, G.; Bangga, G.; Jost, E.; Lutz, T.; Krämer, E. Consistent 3D CFD and BEM simulations of a research turbine considering rotational augmentation. J. Phys. Conf. Ser.
**2018**, 1037, 022024. [Google Scholar] [CrossRef] - Jonkman, J.M.; Buhl, M.L., Jr. FAST User’S Guide; Technical Report No. NREL/EL-500-38230; National Renewable Energy Laboratory: Golden, CO, USA, 2005.
- Marten, D.; Wendler, J.; Pechlivanoglou, G.; Nayeri, C.; Paschereit, C. QBLADE: An open source tool for design and simulation of horizontal and vertical axis wind turbines. Int. J. Emerg. Technol. Adv. Eng.
**2013**, 3, 264–269. [Google Scholar] - Heramarwan, H. Sensitivity of Wind Turbine Loads to Variation of Aerodynamic Polars Predicted by BEM and Free Vortex Approaches. Bachelor’s Thesis, University of Stuttgart, Stuttgart, Germany, 2018. [Google Scholar]
- Marten, D.; Pechlivanoglou, G.; Nayeri, C.; Paschereit, C. Integration of a WT Blade Design tool in XFOIL/XFLR5. In Proceedings of the 10th German Wind Energy Conference (DEWEK 2010), Bremen, Germany, 17–18 November 2010; pp. 17–18. [Google Scholar]
- McCrink, M.; Gregory, J.W. Blade element momentum modeling of low-Re small UAS electric propulsion systems. In Proceedings of the 33rd AIAA Applied Aerodynamics Conference, Dallas, TX, USA, 22–26 June 2015; p. 3296. [Google Scholar]
- Li, L. MATLAB User Manual; The MathWorks, Inc.: Natick, MA, USA, 2001. [Google Scholar]
- Masters, I.; Chapman, J.; Willis, M.; Orme, J. A robust blade element momentum theory model for tidal stream turbines including tip and hub loss corrections. J. Mar. Eng. Technol.
**2011**, 10, 25–35. [Google Scholar] [CrossRef] - Moriarty, P.J.; Hansen, A.C. AeroDyn Theory Manual; National Renewable Energy Laboratory: Golden, CO, USA, 2005.
- Manwell, J.F.; McGowan, J.G.; Rogers, A.L. Wind Energy Explained: Theory, Design and Application; John Wiley & Sons: Hoboken, NJ, USA, 2010. [Google Scholar]
- Sørensen, J.N. General Momentum Theory for Horizontal Axis Wind Turbines; Springer: Berlin, Germany, 2016; Volume 4. [Google Scholar]
- Spera, D.A. Wind Turbine Technology; The American Society of Mechanical Engineers: New York, NY, USA, 1994. [Google Scholar]
- Blazek, J. Computational Fluid Dynamics—Principles and Applications; Butterworth-Heinemann: Oxford, UK, 2015. [Google Scholar]
- Jameson, A. Multigrid algorithms for compressible flow calculations. In Lecture Notes in Mathematics; Springer: Berlin, Germany, 1986; Volume 1228, pp. 166–201. [Google Scholar]
- Favre, A. Equations des gaz turbulents compressibles, part 1 et 2. J. Mech.
**1965**, 4, 391. [Google Scholar] - Hinze, J. Turbulence; McGraw-Hill: New York, NY, USA, 1975; Volume 218. [Google Scholar]
- Lekou, D.; Chortis, D.; Chaviaropoulos, P.; Munduate, X.; Irisarri, A.; Madsen, H.; Yde, K.; Thomsen, K.; Stettner, M.; Reijerkerk, M. Avatar Deliverable d1.2 Reference Blade Design. Technical Report, ECN Wind Energy. 2015. Available online: http://www.eera-avatar.eu/publications-results-and-links/ (accessed on 16 October 2018).
- Bak, C.; Zahle, F.; Bitsche, R.; Kim, T.; Yde, A.; Henriksen, L.; Andersen, P.; Natarajan, A.; Hansen, M. Design and Performance of a 10 MW Turbine; Technical Report; Technical University of Denmark: Lyngby, UK, 2013. [Google Scholar]
- Pointwise Inc. Gridgen Version 15 User Manual; Pointwise Inc.: Fort Worth, TX, USA, 2012. [Google Scholar]
- Kroll, N.; Rossow, C.C.; Becker, K.; Thiele, F. The MEGAFLOW project. Aerosp. Sci. Technol.
**2000**, 4, 223–237. [Google Scholar] [CrossRef] - Aumann, P.; Bartelheimer, W.; Bleecke, H.; Kuntz, M.; Lieser, J.; Monsen, E.; Eisfeld, B.; Fassbender, J.; Heinrich, R.; et al. FLOWer Installation and User Manual; Deutsches Zentrum fur Luft- und Raumfahrt: Cologne, Germany, 2008. [Google Scholar]
- Bangga, G.; Weihing, P.; Lutz, T.; Krämer, E. Hybrid RANS/LES simulations of the three-dimensional flow at root region of a 10 MW wind turbine rotor. In New Results in Numerical and Experimental Fluid Mechanics XI; Springer: Berlin, Germany, 2018; pp. 707–716. [Google Scholar]
- Celik, I.B.; Ghia, U.; Roache, P.J. Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J. Fluids Eng.
**2008**, 130. [Google Scholar] [CrossRef] - Chaviaropoulos, P.; Hansen, M.O. Investigating three-dimensional and rotational effects on wind turbine blades by means of a quasi-3D Navier-Stokes solver. J. Fluids Eng.
**2000**, 122, 330–336. [Google Scholar] [CrossRef] - Bangga, G.; Guma, G.; Lutz, T.; Krämer, E. Numerical simulations of a large offshore wind turbine exposed to turbulent inflow conditions. Wind Eng.
**2018**, 42, 88–96. [Google Scholar] [CrossRef]

**Figure 1.**Rotating annular stream tube at various streamwise positions. The illustration is redrawn with modifications based on Ref [7].

**Figure 4.**Visualization of the sectional airfoils employed in the Advanced Aerodynamic Tools for Large Rotors (AVATAR) blade.

**Figure 5.**Surface mesh and detailed cross-section mesh of the blade. Variables x, y and z represent local coordinate of the blade section in the rotating frame of reference.

**Figure 6.**Grid setup showing blade (purple); spinner and nacelle (red); refinement (yellow) and background grids (green). Variables X, Y and Z represent coordinate system in the inertial frame of reference.

**Figure 7.**Grid density influence on the sectional loads predictions of the generic 10 MW AVATAR blade; (

**a**) normal force, (

**b**) tangential force.

**Figure 8.**Effects of various polar datasets on the accuracy of BEM predictions; (

**a**) normal force, (

**b**) tangential force.

**Figure 9.**Effects of various polar datasets on the accuracy of BEM predictions in terms of (

**a**) ${C}_{L}$ and (

**b**) ${C}_{D}$ and $\alpha $.

**Figure 11.**Tip loss model influence on the 3D polar datasets; (

**a**) normal force, (

**b**) tangential force, (

**c**) axial induction, (

**d**) tangential induction.

**Figure 12.**Effects of interpolation order of the polar data on the sectional force distributions along the blade radius; (

**a**) normal force, (

**b**) tangential force.

**Figure 13.**Effects of blade element discretization for radial-linear interpolation on the sectional force distributions along the blade radius; (

**a**) normal force, (

**b**) tangential force.

**Figure 14.**Effects of blade element discretization for radial-quadratic spline interpolation on the sectional force distributions along the blade radius; (

**a**) normal force, (

**b**) tangential force.

**Figure 15.**Effects of blade element discretization for radial-cubic spline interpolation on the sectional force distributions along the blade radius; (

**a**) normal force, (

**b**) tangential force.

**Figure 16.**Effects of the radial interpolation order on the sectional force distributions along the blade radius; (

**a**) normal force, (

**b**) tangential force.

**Figure 17.**Sectional loads predicted by BEM and CFD for two different wind speeds. 3D polar and cubic-spline interpolation are employed; (

**a**) normal force, (

**b**) tangential force.

Airfoil Thickness [$\mathit{t}/\mathit{c}$] | Airfoil Type |
---|---|

60.0% | Artificial, based on thickest available DU |

40.1% | DU 00-W2-401 |

35.0% | DU 00-W2-350 |

30.0% | DU 97-W300 |

24.0% | DU 91-W2-250 (modified for $t/c=$ 24%) |

21.0% | Based on DU 00-W212, added trailing edge thickness |

**Table 2.**Grid convergence study for the AVATAR blade using the GCI approach. Data are obtained from the URANS calculations.

Parameter | Power | Thrust |
---|---|---|

Value fine | 9.28 × 10${}^{6}$ W | 1.330 × 10${}^{6}$ N |

Value medium | 9.26 × 10${}^{6}$ W | 1.328 × 10${}^{6}$ N |

Value coarse | 9.20 × 10${}^{6}$ W | 1.326 × 10${}^{6}$ N |

Extrapolated rel. error | ||

-fine | 0.12% | 0.27% |

-medium | 0.36% | 0.47% |

-coarse | 1.02% | 0.58% |

Grid convercence index | 0.15% | 0.34% |

$\mathit{\u03f5}$$\mathit{Fn}$ [%] | $\mathit{\u03f5}$$\mathit{Ft}$ [%] | |||||
---|---|---|---|---|---|---|

r = 15 m | r = 60 m | r = 90 m | r = 15 m | r = 60 m | r = 90 m | |

2D Polar | 99.01 | 3.45 | 2.56 | 598.24 | 6.67 | 6.06 |

2D Polar + Stall Delay | 127.80 | 3.19 | 2.56 | 468.88 | 6.48 | 6.06 |

3D Polar | 11.84 | 3.08 | 0.24 | 19.58 | 4.81 | 0.33 |

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**MDPI and ACS Style**

Bangga, G.
Comparison of Blade Element Method and CFD Simulations of a 10 MW Wind Turbine. *Fluids* **2018**, *3*, 73.
https://doi.org/10.3390/fluids3040073

**AMA Style**

Bangga G.
Comparison of Blade Element Method and CFD Simulations of a 10 MW Wind Turbine. *Fluids*. 2018; 3(4):73.
https://doi.org/10.3390/fluids3040073

**Chicago/Turabian Style**

Bangga, Galih.
2018. "Comparison of Blade Element Method and CFD Simulations of a 10 MW Wind Turbine" *Fluids* 3, no. 4: 73.
https://doi.org/10.3390/fluids3040073