# CFD Computation of the H-Darrieus Wind Turbine—The Impact of the Rotating Shaft on the Rotor Performance

## Abstract

**:**

## 1. Introduction

_{0}, to the rotor radius, R, from 1.5% for r

_{0}/R=0.04 to 4.7% for r

_{0}/R=0.16 in comparison with the rotor without tower.

## 2. Characteristics of the VAWT

#### 2.1. Vertical Axis Wind Turbine Concept and Aerodynamic Characteristics

_{T}, is responsible for creating the torque, that is also for the power generated by a given rotor. This aerodynamic force component as well as the normal force, F

_{N}, depend on the position of the rotor, which uniquely defines the azimuth angle θ (Figure 1b). These forces are defined in this work as coefficients

_{0}is the undisturbed flow velocity; R is the rotor radius; q is the air density.

_{x}, and the perpendicular component, U

_{y}.

#### 2.2. Method

^{-5}. The underrelaxation factors for the turbulent kinetic energy, specific dissipation rate, and turbulent viscosity were set to 0.8, 0.8, and 1, respectively [29,30].

## 3. Wind Turbine and Computational Model

#### 3.1. Experimental Test Case

#### 3.2. Wind Turbine Overview

_{0}, was 9.3 m/s. For given rotor operating conditions and for geometric parameters, the Reynolds number of the blade was 170,000. The conceptual model of the tested rotor is shown in Figure 2. This figure also shows the positions of the measuring points behind the rotor in which the velocity was collected. Other geometrical dimensions of the rotor are shown in Figure 3.

#### 3.3. Computational Domain and Boundary Conditions

_{i}= 2 m was created that surrounded the rotor. During simulation, data is transferred between areas via the interface. The remaining dimensions are assumed: distance between the rotor axis and the inlet, L

_{i}= 6 m, and distance between the rotor axis and the outlet, L

_{o}= 14 m. The influence of the diameters D

_{i}, L

_{i}and L

_{o}on the performance of the wind turbine has not been studied in this work. A non-slip wall boundary condition was applied at the airfoil and shaft edges. In order to model smooth side walls of the wind tunnel a slip-wall boundary condition is used by specifying zero shear stress. The dimensions of the computational domain and boundary conditions are shown in Figure 3.

#### 3.4. Mesh

^{-3}mm and the growth rate of subsequent structural grid layers is 1.18. Such thickness of the first layer of the structural grid provides an average value of the dimensionless parameter called wall y

^{+}equal to 0.2. To ensure the best accuracy of flow parameters in the area of the rotor and behind it, the growth of unstructured grid elements was very small equal to 1.02. The number of uniform blade edge divisions is 200 and the shaft is 100. The total number of cells for the reference computing grid is 261,398. Section 4.5 presents the effect of grid density on aerodynamic blade loads calculated.

## 4. Results

#### 4.1. Aerodynamic Blade Loads

_{P}, from 0.411 to 0.401. The largest difference between numerical and experimental results was observed for the θ=130 (deg). The measurement error in this rotor position is also the largest. Numerical studies conducted by Rogowski et al. [33] with the use of a more advanced technique, Scale Adaptive Simulation (SAS), have shown that even for rotors operating in the range of optimal tip speed ratios, the effects typical for dynamic stall can be noticeable. They are, however, possible to detect by using more advanced techniques and using three-dimensional Navier–Stokes equations. Slightly higher results of the calculated normal force compared to the experimental results seem to be justified due to the fact that the analyzed model was two-dimensional, and the blade tip losses were not taken into account in this work. The influence of the rotating shaft in the experiment differs slightly from that obtained in the calculations. The normal force curve appears to be more flat in the downwind part of the rotor. The lack of a visible peak in the experimental curve of the normal force may result from 3D effects, which the two-dimensional numerical model did not include.

#### 4.2. Aerodynamic Wake Characteristics

_{x}, and perpendicular, U

_{y}(Figure 1b). Figure 6 and Figure 7 present profiles of these velocity components averaged over the entire rotation of the rotor. The U

_{x,avr}and U

_{y,avr}symbols were used for the averaged values of these velocity components.

_{x,avr}calculated for both rotors differ slightly compared to experimental results (Figure 6). The differences are slightly lower in the case of the second velocity component, U

_{y,avr}. These velocities are also related to wind speed, V

_{0}. The shapes of the dominant velocity component calculated numerically resemble the Gaussian curve while the velocity profiles measured in the experiment are asymmetrical. In this work, the influence of struts on rotor performance has not been studied. The struts are in fact profiled beams fixing the blades to the shaft. Each rotor blade is attached to the shaft by means of two struts. The struts can change the flow structure downstream behind the rotor and cause asymmetry of velocity profiles. Another possible factor that affects the differences in the calculated and measured velocity profiles may be the turbulence model used (the SST k-ω model).

_{0}for several azimuth positions of the same rotor blade. The numerical results were compared for the rotor with the shaft (Figure 8b) and the clean one (Figure 8a). The figure shows the effect of the shaft, which reduces the flow rate on the blade located in its shadow almost to zero.

_{x}for one azimuth θ=90 deg while Figure 10 shows the distributions of the second component of the velocity field U

_{y}for the same azimuthal position. The width of the aerodynamic wake downstream behind the rotor measured with the PIV technique is greater compared to the numerical results (Figure 9). In the case of the U

_{x}velocity field, the shaft effect is also visible here (Figure 9c). In Figure 10, a larger area of zero velocity U

_{y}is visible in comparison to the experiment. It seems that this drawing illustrates also other three-dimensional flow effects invisible in numerical simulations.

#### 4.3. Revolution Convergence Analysis

_{m}, averaged over the entire rotation of the rotor and the tip speed ratio is called the rotor power coefficient C

_{P}. This is an important physical quantity that allows to evaluate the aerodynamic efficiency of the wind turbine. Figure 13 shows the relation of the rotor power coefficient as a function of the number rotor revolutions simulated. It is worth noting that when the effect of initial conditions subsides, the power coefficient of the clean rotor is constant while in the case of a rotor with a shaft it is almost constant. The clean rotor achieves a power coefficient of 0.4109 while the shafted rotor of 0.401.

#### 4.4. Impact of Time Step Size

^{-3}was obtained whereas for the smallest angle decrement Δθ=0.01 deg the minimum convergence level was 10

^{-5}. During the research, it turned out that the selection of the appropriate time step size has the greatest impact on the estimation of the aerodynamic blade loads of the blade moving in the rotor shaft shadow, Figure 16a,b. The influence of the time step size on the rotor power coefficient is shown in Figure 17. Initially, as the time step size decreases, the power coefficient increases. This is related to a better estimation of the tangential blade loads in the upwind part of the rotor. Further reduction of the time step size leads to a reduction in the power coefficient which is related to the effect of the rotor shaft shadow. Below the time step size corresponding to the angle step size of 0.05 deg, the rotor power coefficient begins to be constant.

#### 4.5. Mesh Convergence Study

## 5. Conclusions

- The SST k-ω turbulence model provides the results of the normal aerodynamic force component that appears to be satisfactory by comparing it with experimental results. However, slightly overestimated results of this force component may be due to 3D effects, which are not included in this work.
- The reason why the calculated velocity profiles (the velocity component parallel to the wind direction) downstream behind the rotor are not asymmetrical as in the case of the experimental studies it is not entirely clear. One possible reason is the simplification of the numerical model.
- The results of the second velocity component profiles agree much better with experimental research.
- The flow field around the wind turbine rotor is highly three-dimensional. The occurrence of flow separation is very likely in such conditions that are not favorable for URANS approach. Nevertheless, for the two-equation k-ω SST turbulence model and the URANS model, that were used here, the instantaneous velocity fields are consistent with the PIV studies.
- The influence of the rotating shaft is visible mainly in the central part of the velocity profiles and rapidly decreases with the distance downstream from the axis of rotation.
- The drop in the mean velocity for each U
_{x}velocity profile is linear for six distances x/R downstream behind the rotor from 1.5 to 4.0. The average value of the velocity component parallel to the wind direction decreased by 13% for the given x/R range. - The rotor in a non-shaft configuration achieves a power coefficient of 2.468% compared to a rotor equipped with a shaft.
- The frequency of the aerodynamic force acting on the shaft is 113.6% higher compared to the frequency of aerodynamic force of the rotor blade.
- Ten full rotor revolutions are sufficient to obtain repeatable results of the torque coefficient and almost constant values of the averaged rotor power coefficients. However, in order to obtain appropriate velocity profiles at the distance of 4R downstream behind the rotor, 15 full rotor revolutions are required for simulation.
- The selection of the appropriate time step size has the greatest impact on the estimation of the aerodynamic blade loads of the blade moving in the rotor shaft. If the time step size is too large, the shaft influence is invisible. Below the time step size corresponding to the angle step size of 0.05 degrees, the rotor power coefficient begins to be constant.

## Funding

## Conflicts of Interest

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**Figure 1.**H-Darrieus wind turbine rotor and analyzed quantities. (

**a**) Silhouette of the H-type Darrieus wind turbine; (

**b**) Aerodynamic forces acting on the wind turbine blade and velocity components in the aerodynamic wake downstream behind the rotor.

**Figure 4.**Grid distribution. (

**a**) Mesh density in the rotor area; (

**b**) Mesh around the blade; (

**c**) Grid near the rotating shaft.

**Figure 6.**Velocity profiles of the U

_{x}component at a few x/R locations downstream behind the rotor.

**Figure 7.**Velocity profiles of the U

_{y}component at a few x/R locations downstream behind the rotor.

**Figure 8.**Contour maps of the magnitude velocity around one blade for seven azimuthal positions given for (

**a**) the rotor without shaft; (

**b**) the rotor with shaft; (

**c**) PIV [27].

**Figure 9.**Contour maps of the U

_{x}velocity component, shown for (

**a**) PIV [26]; (

**b**) the rotor without shaft; (

**c**) the rotor with shaft.

**Figure 10.**Contour maps of the U

_{y}velocity component, shown for (

**a**) PIV [26]; (

**b**) the rotor without shaft; (

**c**) the rotor with shaft.

**Figure 11.**Aerodynamic forces for example rotor rotations. (

**a**) Normal force coefficient for clean rotor; (

**b**) Tangential force coefficient for clean rotor; (

**c**) Normal force coefficient for the shafted rotor; (

**d**) Tangential force coefficient for the shafted rotor.

**Figure 12.**Torque coefficient from the entire rotor for: (

**a**) the rotor with shaft; (

**b**) the clean rotor.

**Figure 14.**Velocity profiles for example rotor rotations: (

**a**) U

_{x}velocity component; (

**b**) U

_{y}velocity component.

**Figure 15.**Averaged velocity profiles for different positions downstream behind the rotor for (

**a**) U

_{x}velocity component; (

**b**) U

_{y}velocity component.

**Figure 16.**Influence of the time step size that corresponds to the angle step size Δθ on the aerodynamic blade loads: (

**a**) normal and (

**b**) tangential.

**Figure 18.**Influence of mesh density on the rotor power coefficient and the total number of grid elements.

Parameter | Value |
---|---|

Number of blades, N | 2 |

Rotor diameter, D=2R | 1 m |

Chord length, c | 0.06 m |

Solidity, Nc/R | 0.24 |

Blade airfoil | NACA0018 |

Rotor shaft diameter, D_{S} | 0.04 m |

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**MDPI and ACS Style**

Rogowski, K. CFD Computation of the H-Darrieus Wind Turbine—The Impact of the Rotating Shaft on the Rotor Performance. *Energies* **2019**, *12*, 2506.
https://doi.org/10.3390/en12132506

**AMA Style**

Rogowski K. CFD Computation of the H-Darrieus Wind Turbine—The Impact of the Rotating Shaft on the Rotor Performance. *Energies*. 2019; 12(13):2506.
https://doi.org/10.3390/en12132506

**Chicago/Turabian Style**

Rogowski, Krzysztof. 2019. "CFD Computation of the H-Darrieus Wind Turbine—The Impact of the Rotating Shaft on the Rotor Performance" *Energies* 12, no. 13: 2506.
https://doi.org/10.3390/en12132506