# Development and Evaluation of an Aerodynamic Model for a Novel Vertical Axis Wind Turbine Concept

## Abstract

**:**

## 1. Introduction

## 2. Aerodynamic Performance Model

#### 2.1. Blade Element Loads

_{c}) at each corresponding node is calculated for each blade azimuth position (θ) using Equations (1–3) (as described in [18]):

_{f turb}, is approximated by assuming the turbulent boundary-layer growth over an equivalent flat plate. Equation (1) is used to approximate the strut lift coefficient.

_{1}to n

_{j}, that pass through each lateral streamtube at the current height interval. The function $f\left(\theta \right)$ is evaluated from the nodal normal force coefficient (${C}_{N}$) and tangential force coefficient (${C}_{T}$) at blade azimuth positions in the range θ = −90° to +90° in increments ∆θ = 5° (i.e., for 37 lateral streamtubes). Consequently, the upwind induced velocity can be updated using Equation (9) (${a}_{u}$ = 1 is assumed for the initial iteration) and an iterative procedure used to update the induced velocity until convergence is achieved:

#### 2.2. Wind Profiles

_{∞}) with height (h), relative to a reference wind velocity (U

_{o}) measured at a height (h

_{o}) given by:

_{o}) specified for each experimental wind turbine, the local freestream wind speed is evaluated assuming a wind shear exponent, α = 0.16, being representative of open level terrain with no trees, typical of these experimental facilities.

#### 2.3. Three-Dimensional Aspects

_{D}

_{(J)}, is added to the profile and induced drag, though this increment is comparatively small.

_{T}is the tower diameter and D

_{R}is the maximum rotor diameter at the given height. Using this simple tower wake correction, Figure 3 shows that the predicted power is in very good agreement with measured data over most wind speeds at 34 rpm. All calculations presented in this paper include the 3D considerations for tip lift losses, induced and junction drag and tower losses as appropriate.

#### 2.4. Dynamic Flow Considerations

- The actual kinematics of the DS process such as the time delay effects on leading edge pressure response, vortex formation, and vortex shedding are modelled (e.g., Beddoes-Leishman model [26]);
- The mechanics of the DS process are neglected, and the characteristics of the lift curve are modelled (e.g., ONERA model [27]);
- A reference pitch angle is introduced that mimics the effective pitch angle under dynamic conditions (e.g., Gormont model [13]).

_{M}= 1.8. These modified lift and drag coefficients are calculated using Equations (20) and (21) respectively:

_{M}= 6, which gave good agreement between the predicted and experimental performance of the SNL 17m diameter Darrieus turbine. A further adaptation proposed by Brochier et al. [28] neglects the effects of dynamic stall within a range of azimuth angles due to increased turbulence levels that can delay the occurrence of dynamic stall.

_{M}) is a function of section thickness, with A

_{M}= 6 for blades with 15% thick sections and A

_{M}= ∞ for 18% thick sections.

_{M}is also a function of blade chord and suggests alternative values based on calculations for three Φ-shaped turbines (also included in the study by Masson et al. [18]) and two H-shaped turbines with rated powers in the range 100–500 kW. In addition, this study has identified a further modification to the Gormont model that is more appropriate for H-shaped rotors in particular, and neglects dynamic lift and drag for negative pitch rates by adopting:

## 3. Performance Model Results

Turbine | RPM | Rotor diameter (m) | Section t/c | Mean chord (m) | Solidity | Suggested A_{M} | DS |
---|---|---|---|---|---|---|---|

VAWT-260 | 33 | 19.5 | 0.18 | 1.02 | 0.105 | 6 | On |

VAWT-850 | 13.6 | 35 | 0.18 | 1.84 | 0.105 | 11 | On |

NRC 24m | 29.4 | 24 | 0.18 | 0.61 | 0.1 | 3.6 | On |

NRC 24m | 36.6 | 24 | 0.18 | 0.61 | 0.1 | 3.6 | On |

SNL 17m | 42.2 | 16.6 | 0.15 | 0.61 | 0.14 | 6 | On |

SNL 17m | 50.6 | 16.6 | 0.15 | 0.61 | 0.14 | 6 | On |

SNL 34m | 28 | 34 | 0.18/0.21 | 1.03 | 0.13 | - | Off |

SNL 34m | 34 | 34 | 0.18/0.21 | 1.03 | 0.13 | - | Off |

SNL 34m | 38 | 34 | 0.18/0.21 | 1.03 | 0.13 | - | Off |

- DS neglected (no DS);
- original Gormont implementation [Equation (17)] for negative pitch rates (K
_{1}= −0.5); - proposed modification [Equation (22)] for negative pitch rates (K
_{1}= 0.0).

_{M}= 6, gave good agreement between the predicted and experimental data for this turbine. This was also observed using the present model and power results are compared for this turbine in Figure 6 using the original Gormont implementation for negative pitch rates (i.e., K

_{1}= −0.5 in Equation (17) and A

_{M}= 6) and using the modified implementation (i.e., K

_{1}= 0.0 in Equation (22) and A

_{M}= 3.6). The figure shows good agreement between measured and predicted power using the original Gormont implementation except for wind speeds over approximately 14 and 18 m/s for rotational speeds of 42.2 and 50.6 rpm respectively, where the model begins to under-predict the power when the blades encounter deep stall. For this turbine the proposed DS modification over-predicts the power.

_{N}, is under-predicted. Momentum theory suggests that C

_{N}= 0 when the blade is parallel with the wind direction (i.e., for blade azimuth positions −90°, +90°, and +270°) for an untwisted symmetric blade section, but experimental data indicates that this is not the case indicating a lag effect that is not modeled using the present model.

**Figure 7.**Sandia 17 m Φ-rotor variation of equatorial normal force coefficient with blade position (38.7 rpm).

_{N}magnitude is not well matched, corresponding to an under-prediction of power at this wind speed and the slightly higher rotational speed of 42.2 rpm (see Figure 6).

_{M}= 3.6, giving good agreement with measured power. The original Gormont model results in an under prediction of power.

_{M}= 6. Clearly dynamic stall has a significant effect on power for wind speeds above ~8 m/s. Furthermore, the suggested modification of K

_{1}= 0 for negative pitch rates gives an improved comparison of power over most wind speeds, with the value suggested by Gormont (K

_{1}= −0.5) under-predicting power.

_{M}= 11, a good representation of the power curve shape is achieved and reasonable agreement of peak power. As for the smaller VAWT-260 H-rotor the proposed modification to the Gormont model improves the prediction of power relative to the original implementation at all wind speeds above 6 m/s.

_{M}= 6. Although there is some scatter in the measured data there is a clear trend that is reasonably well predicted except at low wind speeds. This 5 kW prototype is not efficient due to the large losses from multiple junctions and the induced drag and lift losses from the low aspect ratio blades. Using the present performance model within a multi-disciplinary optimisation procedure the concept was developed for a 10 MW offshore VAWT. These designs proposed a novel “sycamore” shaped rotor with fewer high aspect ratio blades, and the potential to lower the cost of energy compared with conventional offshore turbines and was described in detail in [34].

## 4. Discussion and Recommendations

_{M}= 6, giving good agreement with measured power except at higher wind speeds. Masson et al. [18] suggested that the Masse damping coefficient is a function of the blade aerofoil geometry and in particular the thickness/chord ratio, recommending A

_{M}= ∞ for the NRC/Hydro-Quebec 24 m diameter Φ-shaped turbine with the thicker NACA 0018 section. The present study would suggest that for this section, an appropriate Masse coefficient is also a function of the blade chord (c). Results also indicate that DS is more significant for the H-shaped rotors than for the Φ-shaped rotors, and particularly for the VAWT-850 machine, though the configuration shape does not influence the damping coefficient. For the three turbines considered with the NACA 0018 section, the optimum Masse damping coefficient can be approximated using:

## 5. Conclusions

## Acknowledgments

## Conflict of Interest

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**MDPI and ACS Style**

Shires, A.
Development and Evaluation of an Aerodynamic Model for a Novel Vertical Axis Wind Turbine Concept. *Energies* **2013**, *6*, 2501-2520.
https://doi.org/10.3390/en6052501

**AMA Style**

Shires A.
Development and Evaluation of an Aerodynamic Model for a Novel Vertical Axis Wind Turbine Concept. *Energies*. 2013; 6(5):2501-2520.
https://doi.org/10.3390/en6052501

**Chicago/Turabian Style**

Shires, Andrew.
2013. "Development and Evaluation of an Aerodynamic Model for a Novel Vertical Axis Wind Turbine Concept" *Energies* 6, no. 5: 2501-2520.
https://doi.org/10.3390/en6052501