- Email: [email protected]
Effect of airfoil and solidity on performance of small scale vertical axis wind turbine using three dimensional CFD model
Accepted Manuscript Effect of airfoil and solidity on performance of small scale vertical axis wind turbine using three dimensional CFD model Abhishek Subramanian, S. Arun Yogesh, Hrishikesh Sivanandan, Abhijit Giri, V. Madhavan, M. Vivek, V. Ratna Kishore PII:
S0360-5442(17)30875-7
DOI:
10.1016/j.energy.2017.05.118
Reference:
EGY 10926
To appear in:
Energy
Received Date: 2 January 2017 Revised Date:
12 May 2017
Accepted Date: 18 May 2017
Please cite this article as: Subramanian A, Yogesh SA, Sivanandan H, Giri A, Madhavan V, Vivek M, Ratna Kishore V, Effect of airfoil and solidity on performance of small scale vertical axis wind turbine using three dimensional CFD model, Energy (2017), doi: 10.1016/j.energy.2017.05.118. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Effect of Airfoil and Solidity on Performance of Small Scale Vertical Axis Wind Turbine using Three Dimensional CFD Model Abhishek Subramanian, S Arun Yogesh, Hrishikesh Sivanandan, Abhijit Giri, Madhavan V., Vivek M., V. Ratna Kishore1 Department of Mechanical Engineering, Amrita School of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, India Email: [email protected],[email protected] Phone: +91-8122957821, Fax: +91-422-2686274
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Abstract
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This paper presents a study on the effect of solidity and airfoil profile on the performance of
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Vertical Axis Wind Turbines (VAWTs). A 1.1 kW commercially viable Darrieus VAWT was
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studied using ANSYS Fluent. Four different airfoils – NACA 0012, NACA 0015, NACA
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0030 and AIR 001 – were considered in the analysis. The tip speed ratios (λ) were varied
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from 1 to 2.5 with an incoming wind velocity of 10 m/s. It was observed that NACA 0030
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performed better at lower values of λ due to long duration of attached flow; while NACA
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0012 performed better at λ > 1.8 with a wider range of λ. The shed vortex dissipates much
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faster for thinner airfoils than for thicker airfoils at higher values of λ. Two bladed VAWTs
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generated more power than the three bladed turbines. This indicated that turbines with lower
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solidity perform better at high λ.
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Keywords: VAWT, TSR, solidity, airfoil, Darrieus
23 Nomenclature
LES PB PW
H R HAWT VAWT URANS
1
α
Blade cord Coefficient of moment Coefficient of power Computational Fluid Dynamics
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c Cm CP CFD
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∆t θ λ ρ
Large Eddy Simulation Blade power (three blades) Wind power
µ µt ω σ
Height of Wind Turbine Radius of Wind Turbine Horizontal axis wind turbine Vertical axis wind turbine Unsteady Reynolds Average Navier Strokes
y+
U∞ N
Angle of attack Time step size Azimuth angle Tip speed ratio (TSR),
Rotor angular speed Solidity Dimensionless wall distance Free stream Wind velocity Number of Blades
Corresponding author - [email protected], [email protected]
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Rω U ∞
Density Dynamic viscosity Turbulent viscosity
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AIRfoil
NACA
National Advisory Committee for Aeronautics
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1. INTRODUCTION
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The need for sustainable sources of energy is growing by the day. Conventional renewable
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sources of energy require large initial financial investments. Due to this, small scale energy
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generation techniques are sought after. Therefore, Vertical Axis Wind Turbines (VAWTs)
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are rising to prominence in this regard. In addition to being omnidirectional and easy to
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maintain [1], various recent studies have shown that VAWTs perform better in urban areas
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when compared to HAWTs [1-4]. The performance of these VAWTs needs to be analysed by
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predicting their characteristics and fundamental understanding for flow field around these
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wind turbines. Various methods have been used to predict the performance of VAWTs of
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which Computational Fluid Dynamics (CFD) analysis is a dependable and accurate technique
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[5]. Performing CFD calculations provides knowledge of the flow along with
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necessary details which can help in better understanding of VAWTs.
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Two dimensional CFD analyses is computationally fast but it comes at the cost of accuracy.
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This is because, the three dimensional effects such as tip vortices and the struts are neglected
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in the 2D case. Extensive research has been done using 2D CFD modelling [6-10]. H-type
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Darrieus VAWT was modeled and simulated using ANSYS Fluent solver by Lanzafame et al.
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[6]. The results obtained were in good agreement with experimental observations and they
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demonstrated that the transition SST turbulence model accurately predicts the flow behavior
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of wind around for small-scale turbines.
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Modifications to the blade geometry have also yielded good results. It was observed that
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symmetric airfoils had a better power coefficient compared to their non-symmetric
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counterparts, as demonstrated by Mohamed [7] by comparing 20 different airfoil profiles.
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The realizable k-ε turbulence model was used for this study. The author also showed that
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thinner airfoils performed better than thicker ones at higher values of λ. These observations
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were in line with those made by Danao et al. [8] who demonstrated that blade thickness had a
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significant effect on performance. The computational model used by this author was
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validated using oscillating airfoil profile. Xiao et al. [9] used modified blades with fixed and
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oscillating flaps. They studied Vertical Axis Tidal Turbines with NACA 0018 as its base
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blade profile. Computed results obtained by them, show that under certain conditions of flow
all the
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ACCEPTED MANUSCRIPT and flap geometry, the power coefficient reaches 28% enhancement. This has been found to
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be due to the effective flow separation suppression and vortex control by utilizing a fixed
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and oscillating flap. Armstrong et al. [10] performed flow visualization on an H-type
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Darrieus vertical axis wind turbine with both straight and canted blades at Re = 500,000 and
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above. The straight blades experienced flow reversal on the inner surface at the peak power
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tip speed ratio of λ = 1.6, irrespective of azimuthal angle. This behavior agreed with flow
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visualizations obtained at lower solidities and Re. The flow behavior observed in canted
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blades was very different from that seen with straight blades. Much less flow separation was
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observed at the peak power tip speed ratio of λ = 2.15 as against that seen with straight blades
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at the same tip speed ratios, resulting in better performance. Li et al. [11] investigated the
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efficacy of the 2.5D LES approach in the aerodynamic study of a straight bladed VAWT. It
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was called 2.5D approach because only a short segment of airfoil blades in the span wise
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direction was modelled. 2.5D LES model showed a better agreement with the experimental
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results vis-à-vis the 2D and 2.5D URANS models and it also provided a more realistic
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description of the aerodynamic details in both the single static airfoil and the rotating straight
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bladed VAWT. However, at high λ, 2.5D LES only showed a fair agreement with the
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experimental results. None of the three CFD approaches used by the authors could predict the
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tangential force accurately in the downwind zone at a higher value of λ. Hand et al. [12] has
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studied dynamic stall phenomenon over VAWT airfoils using 2D URANS model. It was
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observed that airfoil tangential coefficient decreases as the freestream turbulence intensity
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increases.
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A 3D analysis takes more variations of fluid flow characteristics into account vis-a-vis its 2D
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counterpart, thereby providing results with higher accuracy. However, the time taken for
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computation of 3D models is much higher. A comparison between 2D and 3D simulation by
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Hamada et al. [13] showed that there was a large drop in average torque acting on the blades
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in the 3D model. They concluded that this is due to a very strong effect of blade-tips and the
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additional drag from the support arms. The obstructed flow due to the shaft and the flow
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interactions caused by support arms also contribute to the blade performance reduction in the
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leeward path. Castelli [14] investigated a 3D model of a straight bladed VAWT. A
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dependence of aerodynamic displacements on the vertical coordinate of the blade section was
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registered for downwind blade azimuthal positions, suggesting a variation of blade
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contributions to rotor torque along the blade span wise direction. Performances and flow
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fields for a wind turbine with unconventional arms geometry were numerically computed by
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turbulence model. It has been shown that the presence of inclined/profiled arms increases the
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average value (per revolution) of performance coefficient.
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Variation of blade geometry in 3D also showed a trend similar to that observed using 2D
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modelling. It was observed by Eboibi et al. [16] that thinner airfoil profiles performed better
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due to their stalling at a higher angle of attack and lift coefficient. The solidity of the turbine
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also played a major role in the performance. It was observed that the wake effect increases
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with solidity, causing earlier stalling of the blade. However, the amount of kinetic energy
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absorbed from the wind was low at very low solidities. The optimum solidity lies in the range
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of 0.4 to 0.8 as reported by Mohamed [7] and Eboibi et al. [16]. Lam and Peng [17] studied
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the near and far wakes of a two-straight-bladed VAWT using 2D and 3D CFD models.
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Turbulence is modeled using SST-kω and Detached Eddy Simulation (DES). They found that
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stream-wise velocity recovery of 75% occurs about 10 D downstream on wind turbine and
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wake becomes asymmetry as the downstream distance increased. Elkhoury et al. [18] has
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performed combined experimental and numerical analyses on performance of a micro VAWT
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with variable-pitch. The four-bar-linkage variable-pitch VAWT was found to be giving better
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performance compared to fixed-pitch VAWT.
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From the literature survey conducted by the authors, it has been concluded that the analysis of
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VAWTs is complex due to the continuous variation in the angle of attack of wind. Also, it
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can be seen based on literature survey, most of computational models were 2D and it is
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essential to use 3D CFD model to predict the performance of Vertical axis wind turbine
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properly. The effect of these parameters has not been studied using 3D model extensively
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especially in the case of actual scale wind turbines. Three dimensional simulations can help
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understand the effect important parameters like blade geometry and solidity performance of
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VAWT more accurately. The objective of the current analysis is to study effect of airfoil
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profile and solidity by changing the number of blades for a given chord length upon the
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performance of a 1.1 kW commercially viable VAWT using CFD simulations. Three
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standard NACA airfoil profiles and an optimized profile for wind turbine applications are
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chosen for the present investigation. Simulations were performed for TSR, λ ranging from 1
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to 2.5. According to the survey done by the authors, the 2D and 2.5D simulations were not
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capable of predicting the performance accurately especially at higher values of λ as they do
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not capture the effects of blade tips. It is thus more appropriate to study the same using three
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model against experimental results available in the literature.
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In section 2, the turbine geometry and various airfoil blade profiles used in the present study
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are described. In the next section, details of computational domain, grid, boundary conditions
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and methodology has been presented. In section 4, computational results have been validated
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with experimental data available in the literature. In section 5, initially effect of airfoil on
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performance parameter, Cp is presented along with reasoning based vorticity contours. After
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that, effect of solidity (based on number of blades) on performance of VAWT has analyzed.
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2. PROBLEM DESCRIPTION
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This work involves the numerical analysis of a straight, three bladed H-type Darrieus VAWT.
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The turbine model considered for the analysis is taken from McLaren [19] and is as shown in
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Fig. 1. The turbine has a height and radius of 3m and 1.35 m. The central hub is 200 mm in
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diameter. The blades have NACA 0015 profile and struts have been neglected for simplicity
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of analysis.
[Figure 1]
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The effect of airfoil profiles has been studied using four different airfoils – NACA 0012,
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NACA 0015, NACA 0030 and AIR 001 [20] as shown in Fig. 2. AIR 001 is an optimized
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airfoil designed to provide optimal performance of VAWTs at low solidities. The
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performance of this optimized airfoil has been compared with conventional symmetric
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NACA profiles. The effect of solidity has been investigated by comparing 2 bladed and 3
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bladed VAWTs for NACA 0012 and NACA 0030 profiles with a fixed chord length. The
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details of the turbine are summarized in Table 1. ANSYS Fluent solver has been used to
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study the said parameters for λ ranging from 1 to 3.
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[Table 1]
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[Figure 2]
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3. NUMERICAL MODEL
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For an isothermal, 3D incompressible flow, the governing equations are the conservation of
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mass and the conservation of momentum given by equations (1) and (2) respectively. Since 5
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the flow velocities in the domain are much smaller than sound velocity, it can be assumed
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that the density remains constant throughout the flow field.
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r ∇⋅v = 0
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(1)
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rr ur ∇ ⋅ vv = −∇p + ∇. τ + ρ g (2)
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where
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τ = ( µ + µt ) ∇ v + ∇ v
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ur r Where is the density, v is the velocity, g is acceleration due to gravity, p is the pressure, τ
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is the stress tensor, µ is the dynamic viscosity, µt is the turbulent viscosity closed by a suitable
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turbulence model and I is an identity matrix. The solution dependence on turbulence model is
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discussed in the subsequent section.
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As the problem involves flow over a rotating solid, the sliding mesh technique available in
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the solver has been used. A localized meshed fluid zone close to the turbine is rotated with
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the angular velocity of the turbine with a region around it is maintained stationary. Thus the
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computational domain has been divided into two sub domains – the inner cylindrical rotating
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zone and the outer cuboidal stationary zone whose 2D view is shown in Fig. 3 (a).
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The rotating zone has been identified in the figure. Only one half of the turbine has been
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modeled due to its symmetric geometry in order to reduce the computation time. Modeling
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and meshing of the flow domain is done using GAMBIT. Fig. 3 (b) shows a 3D
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representation of the meshed domains.
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The mesh has been refined around the blade wall (as shown in figure 3 (c)) with the total
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number of cells being 2.8 million. Each blade when modelled in 2D has been meshed using a
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control circle to capture the effects of curvature of the blade properly. Each of these circles
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had about 3200 cells in a single plane. This has been done so that the separation phenomena
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are captured effectively. 6
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Figure 3 (c) shows the meshing around each blade using prism layers normal to the walls of
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the blade with a first thickness of 0.05 mm. The average y+ that was achieved for the model
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was 2.90 for λ = 2. The blades and shaft are specified to be solid walls with no slip boundary
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condition. Wind velocity has been specified to be 10 m/s at the inlet (ADEH) and the
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pressure at the exit to be 1 atm (at surface BCFG as shown in Fig. 3 (b)). The top surface
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(CDEF) has been specified to be symmetric boundary, and the other sides (ABCD, EFGH
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and ABGH) to have zero shear stress.
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The variation of azimuthal angle (θ) with blade position in 2 bladed and 3 bladed VAWTs is
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shown in Fig. 4 (a) and (b) respectively. The angle has been measured with respect to blade 1
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in the anti-clockwise direction, or the direction of rotation of the VAWT which forms the
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basis for choosing the time step interval. Every simulation is performed till the flow becomes
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cyclic. This has been verified by plotting moment coefficient defined as
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Cm =
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where ρ is the fluid density, U∞ is the flow velocity, R is the radius, H is the height, c is the
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chord length and M is the torque. Fig. 5 shows the variation of Cm with θ for a 2 bladed
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NACA 0015 profile operating at λ = 1.3. It can be seen that they become independent in the
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5th and 6th rotation and thus the average torque for computing the power generated over the
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rotation is computed for the 6th rotation.
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[Figure 5]
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4. VALIDATION
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The numerical solution should be independent of simulation parameters such as mesh size
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and time step duration. The study for time step independence has been done using ∆t
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corresponding to 1° and 2° increment per time step and the turbulence model independence
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was studied using Transition SST and the SST-kω model. For the wind velocity, turbine
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speed and the chord length considered, the Re based on chord length was between 4.23x105
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and 9.42x105, which indicates the flow to be in the transitional region. Thus the Transition
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SST model has been chosen as recommended by Almohammadi et al. [21]. Grid 7
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independence has been studied using 2.8 million and 3.67 million cells. It can be seen that
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there is a good agreement between the chosen models. Fig. 6 (a) shows the comparison
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between 1° and 2° time steps and between the Transition SST and the SST-kω models. Fig. 6
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(b) shows the comparison between fine and coarse mesh. It can be seen that the results
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obtained are almost identical for all entire rotation. [Figure 6]
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Henceforth, all further simulations have been done using time steps corresponding to 2°
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rotation and Transition SST turbulence model with a grid of 2.8 million cells.
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The work reported by McLaren [19] has been chosen for validation of the modelling
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methodology. Validation was carried out based on the power coefficient of the VAWT.
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Power coefficient, Cp is given by
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C p = Pt / Pw
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Where Pt and Pw are the power output of the turbine and the power available in the oncoming
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flow respectively, given by
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1 Pt = ω 2π
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(5)
(6)
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Pw =
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where ω is the angular velocity, R is the radius, N is the number of blades, M is the average
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torque of all blades, dθ is the infinitesimal azimuthal angle element, ρ is the density and H is
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the height of the turbine.
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Fig. 7 shows a comparison of results obtained by McLaren [19], Chandramouli et al. [22] and
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the current data. It can be seen that McLaren’s experimental data and the current results are in
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good agreement with the current results falling well within the error limits ,with a maximum
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deviation of 16.3% corresponding to λ = 0.87. The 2D model used by Chandramouli et al.
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[22] though predicts close to the experimental results at low value of λ but overpredicts as λ
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increases. This over-prediction is due to the inability to predict vortex separations and tip
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vortices which are not captured in 2D analysis.
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5. RESULTS AND DICUSSION
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5.1 Effect of Airfoil Profile
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Simulations were run for 4 different airfoil profiles – NACA 0012, NACA 0015, NACA
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0030 and AIR 001.
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Fig. 8 (a) and (b) show the variation of Cp against λ for the chosen airfoil profiles for 2 bladed
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and 3 bladed VAWTs respectively. It can be seen from Fig. 8 (a) that Cp increases with λ for
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all profiles and decreases after achieving a maximum value. This is at λ = 2.8, 2.2, 2 and 2.5
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for NACA 0012, NACA 0015, NACA 0030 and AIR 001 where Cp = 0.332, 0.373, 0.35 and
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0.346 respectively. Up to λ < 2, NACA 0030 profile (thickest) shows the highest Cp across
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the profiles but at λ > 2, similar behavior is not seen which makes NACA 0030 profile
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inappropriate at higher λ. It can be seen that NACA 0012 peak shifts to the right at higher λ,
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thus proving to be appropriate at higher λ. This has been in line with the observations made
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by Danao et al. [3]. It can also be observed that the optimized airfoil AIR 001 does not work
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well for higher solidities as stated by Ferreira et al. [20]. Similar behavior can be seen with 3
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bladed turbines as well as shown in Fig. 8 (b) but the λ at which maximum Cp is observed,
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shifted to a lower value. It can be seen that these values are 0.253, 0.334, 0.32 and 0.32 for λ
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= 2.5, 2, 1.8 and 2.2 respectively for the profiles of NACA 0012, NACA 0015, NACA 0030
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and AIR 001 respectively.
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[Figure 8]
To investigate the behavior observed in Fig. 8 (a), the variation of moment coefficient of
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blade 1 with θ was analyzed as seen in Fig. 9 (a) and (b). The observed variation in Cm can be
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justified by looking at the flow around the blade at different θ. The major effect seen with the
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VAWT is the blade-vortex interactions in the downwind region.
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[Figure 9]
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It has been observed by Chandramouli et al. [22] that the torque experienced by each blade is
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similar for a given rotation except that they are phase shifted. Thus the torque experienced by
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blade 1 alone has been compared rather than combined torque. In Fig. 9 (a), the Cm peaks
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when the blade is near 180 degrees from the starting point for all three profiles. This indicates
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that the power generated by a blade during upwind is the maximum. NACA 0015 and NACA 9
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0030 profile during the downwind sweep is also significantly higher than the other two
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profiles, which explains the higher average Cp for NACA 0030 in the case of λ = 1.8. In Fig.
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9 (b), a trend similar to that observed in Fig. 9 (a) can be seen. It can be seen that NACA
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0015 attains maximum Cm while the Cm of all three profiles are almost identical in the
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downwind region.
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[Figure 10]
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A comparison of z-vorticity patterns at different sections along the NACA 0012 blades
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operating at λ = 1.8 is shown in Fig. 10. It can be observed that the contours at the symmetry
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plane and mid plane are almost identical while the one near the tip is different due to the
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blade tip interactions. Thus the z-vorticity seen at the symmetry plane extends for
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considerable length of the blade and therefore, the mid plane contours have been used to
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compare across the profiles.
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[Figure 11]
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The z-vorticity contours for 2 bladed NACA 0012 profile and NACA 0030 profile at low λ
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are shown in Fig. 11 (a) and (b) respectively at different azimuthal positions of blade 1. In the
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figure, θ = 0°-180° corresponds to the upwind of blade 1 and θ = 180°-360° corresponds to its
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downwind. Blade 1 at θ = 160° and θ = 180° in Fig. 11 (a) seems to have attached flow for a
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long duration indicating the maximum torque being generated. This has also been confirmed
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from Fig. 9 (a) that blade 1 generates maximum torque at around 180o. A strong vortex is
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seen on the inner side of the airfoil from 220°. As blade 1 moves further, it can be seen that
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the vortex grows, extending over a larger region leading to vortex shedding. This vortex
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shedding resulted in the reduction of the tangential force experienced by the blade and thus in
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lower power, as seen in Fig. 9 (a). In time, the shed vortex disappears due to interaction with
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free stream, and the cycle repeats. In the case of NACA 0030, a pattern similar to that
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observed for the NACA 0012 profile can be observed but the flow remained attached for a
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longer duration and vortex shedding is not seen at 220°, which is seen in the case of NACA
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0012. Thus the blade experiences a higher positive tangential force for a longer duration
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resulting in higher Cp. It can also be seen that the size of the vortex being shed is smaller in
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comparison. The vortex being shed dies down soon because of the weakening of the same
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due to the incoming free stream. All these results indicate that the performance of NACA
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0030 profile is better than NACA 0012 profile at λ = 1.8.
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At λ = 2.5, there is a reversal in performance with NACA 0015 performing better than NACA
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0030. The mid span z-vorticity contours of 2 bladed NACA 0015 profile and NACA 0030
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profile for λ = 2.5 is shown in Fig. 12 (a) and (b) respectively. The vortex shedding in NACA
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0015 starts much later as can be seen from the figures. Although the shed vortex does not die
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down quickly, the interaction with the blade is not seen at all. The shed vortex moves
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downstream and away from the blade’s trajectory. This can be correlated to the higher Cp of
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NACA 0015. In the case of NACA 0030, the shed vortex seems smaller, however, there is
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some interaction with the blade in the downwind. The vortex being shed is dragged on for a
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long duration causing some interaction between blade 1 and the vortex shed by blade 2. The
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power generated is maximum during the upwind sweep, similar to the observations made in
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Fig. 11. Vortex generation starts just before 240°. The shed vortex does not die down soon
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but it stays for a long while. These observations can be correlated to the decrease in Cp when
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compared to the observations made at λ = 1.8. It can also be observed that the Cp generated at
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λ = 2.5 is comparable to the one generated by NACA0012 profile although the Cp of NACA
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0012 profile is slightly higher.
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The x-vorticity at the blade tip is looked into to understand its effect on the performance of
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VAWTs.
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[Figure 13]
Fig. 13 (a) and (b) shows the x-vorticity contours for various planes of NACA 0030 profile at
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λ = 2 and λ = 2.5 respectively. The plots were obtained to capture the tip vortex effects on the
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flow of air around a VAWT. The z-vorticity plots below and very near the tip is not
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significant and thus the x-vorticity is looked into. It can be seen that the tip vortex generation
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and shedding starts at 160° and continues till 280°. The shed vortex from blade 1 interacts
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with blade 2 for λ = 2.5 whereas there is minimal interaction with the vortex at λ = 2. Due to
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this vortex interaction, Cp reduces for λ = 2.5. This shows the significant effect of tip vortex
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on the performance of a VAWT. This clearly suggests that 3D simulations are necessary to
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predict the performance of VAWTs efficiently, as seen in the validation study.
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[Figure 14]
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Fig. 14 (a) and (b) shows the variation of moment coefficient of the NACA 0012, NACA
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0015 and NACA 0030 with angle for λ = 1.8 and λ = 2.5 respectively. These follow the same 11
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pattern as observed in Fig. 9 (a) and (b) but the peaks are comparatively smaller. The
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vorticity contours are looked into to correlate the flow characteristics to the torque
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characteristics. [Figure 15]
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The vorticity contours for 3 bladed NACA 0012 profile and NACA 0030 at low λ are shown
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in Fig. 15 (a) and (b). NACA 0012 behaves similar to the observations made in Fig. 11.
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Attached flow is predominant in the upwind region, where maximum Cp is generated. Vortex
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shedding is observed to begin after 200°. The vortex shed by blade 3 interferes with blade 2
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to a great extent, thereby affecting the torque experienced by blade 2. The free stream wind
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does not suppress the shed vortex soon enough. In the case of NACA 0030, a trend similar to
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NACA 0012 can be seen here. Blades in the upstream seem to have attached flows for a
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longer duration. Vortex shedding starts much later compared to NACA 0012. Also, the size
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of the vortex shed is small. The interaction between vortex shed by blade 3 and blade 2 is less
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as the shed vortex dies down early.
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5.2 Effect of Solidity
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The effect of solidity is compared by changing the number of blades. Fig. 16 (a) and (b) show
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a comparison of Cp for 2, 3 and 4 bladed NACA 0012 and NACA 0030 profiles respectively
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with λ. The 3 bladed VAWT performs better at lower λ and the 2 bladed VAWT performs
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better at higher λ in both cases and with increase of number of blades to 4, performance of
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wind turbine deteriorates. The 2 bladed VAWT has a larger operating range and performs
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best at λ = 2.8 as seen in the case of NACA 0012 where Cp = 0.332 and λ = 2 and in the case
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of NACA 0030 where Cp = 0.35 as opposed to Cp = 0.253 at λ = 2.5 and 0.32 at λ = 1.8
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respectively in the case of 3 bladed VAWTs.
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[Figure 17]
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At higher λ, 3 bladed turbines face higher interactions with the vortex, resulting in 2 bladed
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turbines performing better, as shown in Fig. 17. However, we can see that at lower λ, the 3
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bladed turbines perform better. This is because at higher solidity, the interception of blade
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with the wind is more. Compared to the 2 bladed profiles, vortex generation is higher and
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therefore the vortex-blade interaction is also higher, resulting in lesser power generation
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compared to 2 bladed turbines at high λ.
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CONCLUSIONS
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Based on the observations made on the effect of airfoil profile and solidity on the
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performance of VAWTs, the following conclusions were made.
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1.
The validation study showed that 2D simulations overpredict the values of Cp at high λ. This is due to the inability of 2D models to capture 3D effects such as vortex interactions
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and tip vortices. 2.
Among all the profiles compared, NACA 0030 attained maximum Cp for low tip speed
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ratios. Thicker airfoils performed better at low λ due to long durations of attached flow.
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This resulted in faster vortex shedding and larger positive tangential force. As the λ was
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increased, the Cp of NACA 0012 profile also increased. Thinner airfoils have larger
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operating ranges than the thicker ones. This is because at larger λ, the shed vortex
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dissipated much faster for thinner airfoils than for thicker airfoils, causing more vortex
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interactions for thicker blades. Based on X vorticity contours, It was observed the tip
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vortex generated interaction leads reduction in moment coefficient and hence, reduction
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3. The Cp observed in 2 bladed VAWTs was higher than that of 3 bladed VAWT for a high
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value of λ due to the increased occurrence of vortex interactions with the blades with
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higher solidity. However, at low λ, high solidity VAWTs performed better because the
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interaction of the blades with wind was better.
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REFERENCES
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1. 2.
3.
4.
Mertens, S., Wind energy in the built environment: concentrator effects of buildings. 2006: TU Delft, Delft University of Technology. Ferreira, C.S., G. van Bussel, and G. Van Kuik. 2D CFD simulation of dynamic stall on a vertical axis wind turbine: verification and validation with PIV measurements. in 45th AIAA aerospace sciences meeting and exhibit. 2007. Nevada, Reno. Hofemann, C., C. Simao Ferreira, G. Van Bussel, G. Van Kuik, F. Scarano, and K. Dixon. 3D Stereo PIV study of tip vortex evolution on a vawt. in The proceedings of the European Wind Energy Conference and exhibition EWEC, Brussels, 1-8. 2008. European Wind Energy Association EWEA. Stankovic, S., N. Campbell, and A. Harries, Urban wind energy. 2009: Earthscan.
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Jin, X., G. Zhao, K. Gao, and W. Ju, Darrieus vertical axis wind turbine: Basic research methods. Renewable and Sustainable Energy Reviews, 2015. 42: p. 212-225. Lanzafame, R., S. Mauro, and M. Messina, 2D CFD Modeling of H-Darrieus Wind Turbines using a Transition Turbulence Model. Energy Procedia, 2014. 45: p. 131-140. Mohamed, M., Performance investigation of H-rotor Darrieus turbine with new airfoil shapes. Energy, 2012. 47(1): p. 522-530. Danao, L.A., N. Qin, and R. Howell, A numerical study of blade thickness and camber effects on vertical axis wind turbines. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2012: p. 0957650912454403. Xiao, Q., W. Liu, and A. Incecik, Flow control for VATT by fixed and oscillating flap. Renewable Energy, 2013. 51: p. 141-152. Armstrong, S., A. Fiedler, and S. Tullis, Flow separation on a high Reynolds number, high solidity vertical axis wind turbine with straight and canted blades and canted blades with fences. Renewable energy, 2012. 41: p. 13-22. Li, C., S. Zhu, Y.-l. Xu, and Y. Xiao, 2.5 D large eddy simulation of vertical axis wind turbine in consideration of high angle of attack flow. Renewable energy, 2013. 51: p. 317-330. Hand, B., G. Kelly, and A. Cashman, Numerical simulation of a vertical axis wind turbine airfoil experiencing dynamic stall at high Reynolds numbers. Computers & Fluids, 2017. 149: p. 12-30. Hamada, K., T. Smith, N. Durrani, N. Qin, and R. Howell. Unsteady flow simulation and dynamic stall around vertical axis wind turbine blades. in 46th AIAA Aerospaces Sciences Meeting and Exhibit, Reno, Nevada. 2008. Castelli, M.R., A. Englaro, and E. Benini, The Darrieus wind turbine: Proposal for a new performance prediction model based on CFD. Energy, 2011. 36(8): p. 4919-4934. De Marco, A., D.P. Coiro, D. Cucco, and F. Nicolosi, A Numerical Study on a Vertical-Axis Wind Turbine with Inclined Arms. International Journal of Aerospace Engineering, 2014. 2014. Eboibi, O., L. Howell, and J.M. Edwards. A numerical study of the influence of blade profile and solidity on the performance of vertical axis wind turbines. in 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. 2013. Lam, H.F. and H.Y. Peng, Study of wake characteristics of a vertical axis wind turbine by twoand three-dimensional computational fluid dynamics simulations. Renewable Energy, 2016. 90: p. 386-398. Elkhoury, M., T. Kiwata, and E. Aoun, Experimental and numerical investigation of a threedimensional vertical-axis wind turbine with variable-pitch. Journal of Wind Engineering and Industrial Aerodynamics, 2015. 139: p. 111-123. McLaren, K.W., A numerical and experimental study of unsteady loading of high solidity vertical axis wind turbines. 2011. Ferreira, C.S. and B. Geurts, Aerofoil optimization for vertical-axis wind turbines. Wind Energy, 2014. Almohammadi, K., D. Ingham, L. Ma, and M. Pourkashanian, Effect of Transitional Turbulence Modelling on a Straight Blade Vertical Axis Wind Turbine, in Alternative Energies. 2013, Springer. p. 93-112. Chandramouli, S., T. Premsai, P. Prithviraj, V. Mugundhan, and R.K. Velamati, Numerical Analysis of Effect of Pitch Angle on a Small Scale Vertical Axis Wind Turbine. International Journal of Renewable Energy Research (IJRER), 2014. 4(4): p. 935.
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Figure 1 H-Type Darrieus VAWT
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Figure 2 Representation of Airfoil profiles – (a) NACA 0012; (b) NACA 0015; (c) NACA 0030; and (d) AIR 001
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Figure 3 (a) 2D view of the domain; (b) 3D view of the meshed domains; (c) Fine mesh very close to the blade
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Figure 4 Azimuthal angle, θ in (a) 2 bladed VAWT; and (b) 3 bladed VAWT
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Figure 5 Variation of Cm with θ for 2 bladed NACA 0015 profile operating at λ = 1.3
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Figure 6 (a) Time step independence and turbulence model independence; (b) grid independence
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Figure 7 Benchmarking Studies
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Figure 8 Variation of Cp with λ for (a) 2 bladed airfoil profiles; (b) 3 bladed airfoil profiles
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Figure 9 Variation of moment coefficient of blade 1 with angle for 2 bladed profiles (a) at λ = 1.8; (b) at λ = 2.5
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Figure 10 Comparison of z-vorticity patterns at different locations along the blade height for 2 bladed NACA 0012 at λ = 1.8
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Figure 11 Mid span z-vorticity contours of 2 bladed (a) NACA 0012 profile; and (b) NACA 0030 profile at λ = 1.8
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Figure 12 Mid span vorticity contours of 2 bladed (a) NACA 0015 profile; and (b) NACA 0030 profile at λ = 2.5
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Figure 13 X – Vorticity contours of NACA 0030 profile at various angles for (a) λ = 2; and (b) λ = 2.5
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Figure 14 Variation of moment coefficient with angle for 3 bladed airfoil profiles at (a) λ = 1.8; (b) λ = 2.5
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Figure 15 Mid span vorticity contours of 3 bladed (a) NACA 0012 profile; and (b) NACA 0030 profile at λ = 1.8
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Figure 16 Variation of Cp with λ for 2 bladed , 3 bladed and 4 bladed VAWT with (a) NACA 0012 airfoil; (b) NACA 0030 profile
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Figure 17 Mid plane x-vorticity contours of (a) 2 bladed; and (b) 3 bladed NACA 0030 profiles operating at λ = 2.5
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Chord, c
0.420 m
Diameter of rotor
2.7 m
Frontal area of rotor
8.1 m2
Solidity, σ
0.33, 0.5
Number of blades
2, 3
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Blade profile
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3D simulations account for tip vortices and thus predicts more realistically. Thicker airfoils perform better at lower TSR Thinner airfoils have wider range of operational TSR
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Higher solidity performs better at lower TSR
S0360-5442(17)30875-7
DOI:
10.1016/j.energy.2017.05.118
Reference:
EGY 10926
To appear in:
Energy
Received Date: 2 January 2017 Revised Date:
12 May 2017
Accepted Date: 18 May 2017
Please cite this article as: Subramanian A, Yogesh SA, Sivanandan H, Giri A, Madhavan V, Vivek M, Ratna Kishore V, Effect of airfoil and solidity on performance of small scale vertical axis wind turbine using three dimensional CFD model, Energy (2017), doi: 10.1016/j.energy.2017.05.118. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Effect of Airfoil and Solidity on Performance of Small Scale Vertical Axis Wind Turbine using Three Dimensional CFD Model Abhishek Subramanian, S Arun Yogesh, Hrishikesh Sivanandan, Abhijit Giri, Madhavan V., Vivek M., V. Ratna Kishore1 Department of Mechanical Engineering, Amrita School of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, India Email: [email protected],[email protected] Phone: +91-8122957821, Fax: +91-422-2686274
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Abstract
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This paper presents a study on the effect of solidity and airfoil profile on the performance of
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Vertical Axis Wind Turbines (VAWTs). A 1.1 kW commercially viable Darrieus VAWT was
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studied using ANSYS Fluent. Four different airfoils – NACA 0012, NACA 0015, NACA
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0030 and AIR 001 – were considered in the analysis. The tip speed ratios (λ) were varied
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from 1 to 2.5 with an incoming wind velocity of 10 m/s. It was observed that NACA 0030
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performed better at lower values of λ due to long duration of attached flow; while NACA
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0012 performed better at λ > 1.8 with a wider range of λ. The shed vortex dissipates much
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faster for thinner airfoils than for thicker airfoils at higher values of λ. Two bladed VAWTs
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generated more power than the three bladed turbines. This indicated that turbines with lower
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solidity perform better at high λ.
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Keywords: VAWT, TSR, solidity, airfoil, Darrieus
23 Nomenclature
LES PB PW
H R HAWT VAWT URANS
1
α
Blade cord Coefficient of moment Coefficient of power Computational Fluid Dynamics
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c Cm CP CFD
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∆t θ λ ρ
Large Eddy Simulation Blade power (three blades) Wind power
µ µt ω σ
Height of Wind Turbine Radius of Wind Turbine Horizontal axis wind turbine Vertical axis wind turbine Unsteady Reynolds Average Navier Strokes
y+
U∞ N
Angle of attack Time step size Azimuth angle Tip speed ratio (TSR),
Rotor angular speed Solidity Dimensionless wall distance Free stream Wind velocity Number of Blades
Corresponding author - [email protected], [email protected]
1
Rω U ∞
Density Dynamic viscosity Turbulent viscosity
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AIRfoil
NACA
National Advisory Committee for Aeronautics
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1. INTRODUCTION
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The need for sustainable sources of energy is growing by the day. Conventional renewable
27
sources of energy require large initial financial investments. Due to this, small scale energy
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generation techniques are sought after. Therefore, Vertical Axis Wind Turbines (VAWTs)
29
are rising to prominence in this regard. In addition to being omnidirectional and easy to
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maintain [1], various recent studies have shown that VAWTs perform better in urban areas
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when compared to HAWTs [1-4]. The performance of these VAWTs needs to be analysed by
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predicting their characteristics and fundamental understanding for flow field around these
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wind turbines. Various methods have been used to predict the performance of VAWTs of
34
which Computational Fluid Dynamics (CFD) analysis is a dependable and accurate technique
35
[5]. Performing CFD calculations provides knowledge of the flow along with
36
necessary details which can help in better understanding of VAWTs.
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Two dimensional CFD analyses is computationally fast but it comes at the cost of accuracy.
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This is because, the three dimensional effects such as tip vortices and the struts are neglected
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in the 2D case. Extensive research has been done using 2D CFD modelling [6-10]. H-type
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Darrieus VAWT was modeled and simulated using ANSYS Fluent solver by Lanzafame et al.
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[6]. The results obtained were in good agreement with experimental observations and they
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demonstrated that the transition SST turbulence model accurately predicts the flow behavior
43
of wind around for small-scale turbines.
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Modifications to the blade geometry have also yielded good results. It was observed that
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symmetric airfoils had a better power coefficient compared to their non-symmetric
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counterparts, as demonstrated by Mohamed [7] by comparing 20 different airfoil profiles.
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The realizable k-ε turbulence model was used for this study. The author also showed that
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thinner airfoils performed better than thicker ones at higher values of λ. These observations
49
were in line with those made by Danao et al. [8] who demonstrated that blade thickness had a
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significant effect on performance. The computational model used by this author was
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validated using oscillating airfoil profile. Xiao et al. [9] used modified blades with fixed and
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oscillating flaps. They studied Vertical Axis Tidal Turbines with NACA 0018 as its base
53
blade profile. Computed results obtained by them, show that under certain conditions of flow
all the
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be due to the effective flow separation suppression and vortex control by utilizing a fixed
56
and oscillating flap. Armstrong et al. [10] performed flow visualization on an H-type
57
Darrieus vertical axis wind turbine with both straight and canted blades at Re = 500,000 and
58
above. The straight blades experienced flow reversal on the inner surface at the peak power
59
tip speed ratio of λ = 1.6, irrespective of azimuthal angle. This behavior agreed with flow
60
visualizations obtained at lower solidities and Re. The flow behavior observed in canted
61
blades was very different from that seen with straight blades. Much less flow separation was
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observed at the peak power tip speed ratio of λ = 2.15 as against that seen with straight blades
63
at the same tip speed ratios, resulting in better performance. Li et al. [11] investigated the
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efficacy of the 2.5D LES approach in the aerodynamic study of a straight bladed VAWT. It
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was called 2.5D approach because only a short segment of airfoil blades in the span wise
66
direction was modelled. 2.5D LES model showed a better agreement with the experimental
67
results vis-à-vis the 2D and 2.5D URANS models and it also provided a more realistic
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description of the aerodynamic details in both the single static airfoil and the rotating straight
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bladed VAWT. However, at high λ, 2.5D LES only showed a fair agreement with the
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experimental results. None of the three CFD approaches used by the authors could predict the
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tangential force accurately in the downwind zone at a higher value of λ. Hand et al. [12] has
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studied dynamic stall phenomenon over VAWT airfoils using 2D URANS model. It was
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observed that airfoil tangential coefficient decreases as the freestream turbulence intensity
74
increases.
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A 3D analysis takes more variations of fluid flow characteristics into account vis-a-vis its 2D
76
counterpart, thereby providing results with higher accuracy. However, the time taken for
77
computation of 3D models is much higher. A comparison between 2D and 3D simulation by
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Hamada et al. [13] showed that there was a large drop in average torque acting on the blades
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in the 3D model. They concluded that this is due to a very strong effect of blade-tips and the
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additional drag from the support arms. The obstructed flow due to the shaft and the flow
81
interactions caused by support arms also contribute to the blade performance reduction in the
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leeward path. Castelli [14] investigated a 3D model of a straight bladed VAWT. A
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dependence of aerodynamic displacements on the vertical coordinate of the blade section was
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registered for downwind blade azimuthal positions, suggesting a variation of blade
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contributions to rotor torque along the blade span wise direction. Performances and flow
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fields for a wind turbine with unconventional arms geometry were numerically computed by
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turbulence model. It has been shown that the presence of inclined/profiled arms increases the
89
average value (per revolution) of performance coefficient.
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Variation of blade geometry in 3D also showed a trend similar to that observed using 2D
91
modelling. It was observed by Eboibi et al. [16] that thinner airfoil profiles performed better
92
due to their stalling at a higher angle of attack and lift coefficient. The solidity of the turbine
93
also played a major role in the performance. It was observed that the wake effect increases
94
with solidity, causing earlier stalling of the blade. However, the amount of kinetic energy
95
absorbed from the wind was low at very low solidities. The optimum solidity lies in the range
96
of 0.4 to 0.8 as reported by Mohamed [7] and Eboibi et al. [16]. Lam and Peng [17] studied
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the near and far wakes of a two-straight-bladed VAWT using 2D and 3D CFD models.
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Turbulence is modeled using SST-kω and Detached Eddy Simulation (DES). They found that
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stream-wise velocity recovery of 75% occurs about 10 D downstream on wind turbine and
100
wake becomes asymmetry as the downstream distance increased. Elkhoury et al. [18] has
101
performed combined experimental and numerical analyses on performance of a micro VAWT
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with variable-pitch. The four-bar-linkage variable-pitch VAWT was found to be giving better
103
performance compared to fixed-pitch VAWT.
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From the literature survey conducted by the authors, it has been concluded that the analysis of
105
VAWTs is complex due to the continuous variation in the angle of attack of wind. Also, it
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can be seen based on literature survey, most of computational models were 2D and it is
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essential to use 3D CFD model to predict the performance of Vertical axis wind turbine
108
properly. The effect of these parameters has not been studied using 3D model extensively
109
especially in the case of actual scale wind turbines. Three dimensional simulations can help
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understand the effect important parameters like blade geometry and solidity performance of
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VAWT more accurately. The objective of the current analysis is to study effect of airfoil
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profile and solidity by changing the number of blades for a given chord length upon the
113
performance of a 1.1 kW commercially viable VAWT using CFD simulations. Three
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standard NACA airfoil profiles and an optimized profile for wind turbine applications are
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chosen for the present investigation. Simulations were performed for TSR, λ ranging from 1
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to 2.5. According to the survey done by the authors, the 2D and 2.5D simulations were not
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capable of predicting the performance accurately especially at higher values of λ as they do
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not capture the effects of blade tips. It is thus more appropriate to study the same using three
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model against experimental results available in the literature.
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In section 2, the turbine geometry and various airfoil blade profiles used in the present study
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are described. In the next section, details of computational domain, grid, boundary conditions
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and methodology has been presented. In section 4, computational results have been validated
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with experimental data available in the literature. In section 5, initially effect of airfoil on
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performance parameter, Cp is presented along with reasoning based vorticity contours. After
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that, effect of solidity (based on number of blades) on performance of VAWT has analyzed.
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2. PROBLEM DESCRIPTION
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This work involves the numerical analysis of a straight, three bladed H-type Darrieus VAWT.
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The turbine model considered for the analysis is taken from McLaren [19] and is as shown in
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Fig. 1. The turbine has a height and radius of 3m and 1.35 m. The central hub is 200 mm in
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diameter. The blades have NACA 0015 profile and struts have been neglected for simplicity
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of analysis.
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The effect of airfoil profiles has been studied using four different airfoils – NACA 0012,
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NACA 0015, NACA 0030 and AIR 001 [20] as shown in Fig. 2. AIR 001 is an optimized
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airfoil designed to provide optimal performance of VAWTs at low solidities. The
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performance of this optimized airfoil has been compared with conventional symmetric
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NACA profiles. The effect of solidity has been investigated by comparing 2 bladed and 3
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bladed VAWTs for NACA 0012 and NACA 0030 profiles with a fixed chord length. The
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details of the turbine are summarized in Table 1. ANSYS Fluent solver has been used to
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study the said parameters for λ ranging from 1 to 3.
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[Table 1]
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[Figure 2]
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3. NUMERICAL MODEL
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For an isothermal, 3D incompressible flow, the governing equations are the conservation of
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mass and the conservation of momentum given by equations (1) and (2) respectively. Since 5
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the flow velocities in the domain are much smaller than sound velocity, it can be assumed
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that the density remains constant throughout the flow field.
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r ∇⋅v = 0
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(1)
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rr ur ∇ ⋅ vv = −∇p + ∇. τ + ρ g (2)
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where
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τ = ( µ + µt ) ∇ v + ∇ v
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ur r Where is the density, v is the velocity, g is acceleration due to gravity, p is the pressure, τ
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is the stress tensor, µ is the dynamic viscosity, µt is the turbulent viscosity closed by a suitable
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turbulence model and I is an identity matrix. The solution dependence on turbulence model is
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discussed in the subsequent section.
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As the problem involves flow over a rotating solid, the sliding mesh technique available in
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the solver has been used. A localized meshed fluid zone close to the turbine is rotated with
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the angular velocity of the turbine with a region around it is maintained stationary. Thus the
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computational domain has been divided into two sub domains – the inner cylindrical rotating
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zone and the outer cuboidal stationary zone whose 2D view is shown in Fig. 3 (a).
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The rotating zone has been identified in the figure. Only one half of the turbine has been
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modeled due to its symmetric geometry in order to reduce the computation time. Modeling
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and meshing of the flow domain is done using GAMBIT. Fig. 3 (b) shows a 3D
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representation of the meshed domains.
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The mesh has been refined around the blade wall (as shown in figure 3 (c)) with the total
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number of cells being 2.8 million. Each blade when modelled in 2D has been meshed using a
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control circle to capture the effects of curvature of the blade properly. Each of these circles
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had about 3200 cells in a single plane. This has been done so that the separation phenomena
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are captured effectively. 6
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Figure 3 (c) shows the meshing around each blade using prism layers normal to the walls of
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the blade with a first thickness of 0.05 mm. The average y+ that was achieved for the model
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was 2.90 for λ = 2. The blades and shaft are specified to be solid walls with no slip boundary
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condition. Wind velocity has been specified to be 10 m/s at the inlet (ADEH) and the
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pressure at the exit to be 1 atm (at surface BCFG as shown in Fig. 3 (b)). The top surface
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(CDEF) has been specified to be symmetric boundary, and the other sides (ABCD, EFGH
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and ABGH) to have zero shear stress.
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The variation of azimuthal angle (θ) with blade position in 2 bladed and 3 bladed VAWTs is
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shown in Fig. 4 (a) and (b) respectively. The angle has been measured with respect to blade 1
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in the anti-clockwise direction, or the direction of rotation of the VAWT which forms the
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basis for choosing the time step interval. Every simulation is performed till the flow becomes
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cyclic. This has been verified by plotting moment coefficient defined as
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Cm =
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where ρ is the fluid density, U∞ is the flow velocity, R is the radius, H is the height, c is the
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chord length and M is the torque. Fig. 5 shows the variation of Cm with θ for a 2 bladed
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NACA 0015 profile operating at λ = 1.3. It can be seen that they become independent in the
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5th and 6th rotation and thus the average torque for computing the power generated over the
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rotation is computed for the 6th rotation.
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4. VALIDATION
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The numerical solution should be independent of simulation parameters such as mesh size
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and time step duration. The study for time step independence has been done using ∆t
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corresponding to 1° and 2° increment per time step and the turbulence model independence
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was studied using Transition SST and the SST-kω model. For the wind velocity, turbine
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speed and the chord length considered, the Re based on chord length was between 4.23x105
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and 9.42x105, which indicates the flow to be in the transitional region. Thus the Transition
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SST model has been chosen as recommended by Almohammadi et al. [21]. Grid 7
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independence has been studied using 2.8 million and 3.67 million cells. It can be seen that
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there is a good agreement between the chosen models. Fig. 6 (a) shows the comparison
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between 1° and 2° time steps and between the Transition SST and the SST-kω models. Fig. 6
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(b) shows the comparison between fine and coarse mesh. It can be seen that the results
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obtained are almost identical for all entire rotation. [Figure 6]
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Henceforth, all further simulations have been done using time steps corresponding to 2°
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rotation and Transition SST turbulence model with a grid of 2.8 million cells.
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The work reported by McLaren [19] has been chosen for validation of the modelling
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methodology. Validation was carried out based on the power coefficient of the VAWT.
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Power coefficient, Cp is given by
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C p = Pt / Pw
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Where Pt and Pw are the power output of the turbine and the power available in the oncoming
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flow respectively, given by
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1 Pt = ω 2π
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(5)
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Pw =
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where ω is the angular velocity, R is the radius, N is the number of blades, M is the average
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torque of all blades, dθ is the infinitesimal azimuthal angle element, ρ is the density and H is
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the height of the turbine.
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Fig. 7 shows a comparison of results obtained by McLaren [19], Chandramouli et al. [22] and
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the current data. It can be seen that McLaren’s experimental data and the current results are in
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good agreement with the current results falling well within the error limits ,with a maximum
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deviation of 16.3% corresponding to λ = 0.87. The 2D model used by Chandramouli et al.
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[22] though predicts close to the experimental results at low value of λ but overpredicts as λ
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increases. This over-prediction is due to the inability to predict vortex separations and tip
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vortices which are not captured in 2D analysis.
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5. RESULTS AND DICUSSION
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5.1 Effect of Airfoil Profile
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Simulations were run for 4 different airfoil profiles – NACA 0012, NACA 0015, NACA
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0030 and AIR 001.
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Fig. 8 (a) and (b) show the variation of Cp against λ for the chosen airfoil profiles for 2 bladed
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and 3 bladed VAWTs respectively. It can be seen from Fig. 8 (a) that Cp increases with λ for
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all profiles and decreases after achieving a maximum value. This is at λ = 2.8, 2.2, 2 and 2.5
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for NACA 0012, NACA 0015, NACA 0030 and AIR 001 where Cp = 0.332, 0.373, 0.35 and
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0.346 respectively. Up to λ < 2, NACA 0030 profile (thickest) shows the highest Cp across
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the profiles but at λ > 2, similar behavior is not seen which makes NACA 0030 profile
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inappropriate at higher λ. It can be seen that NACA 0012 peak shifts to the right at higher λ,
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thus proving to be appropriate at higher λ. This has been in line with the observations made
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by Danao et al. [3]. It can also be observed that the optimized airfoil AIR 001 does not work
243
well for higher solidities as stated by Ferreira et al. [20]. Similar behavior can be seen with 3
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bladed turbines as well as shown in Fig. 8 (b) but the λ at which maximum Cp is observed,
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shifted to a lower value. It can be seen that these values are 0.253, 0.334, 0.32 and 0.32 for λ
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= 2.5, 2, 1.8 and 2.2 respectively for the profiles of NACA 0012, NACA 0015, NACA 0030
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and AIR 001 respectively.
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[Figure 8]
To investigate the behavior observed in Fig. 8 (a), the variation of moment coefficient of
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blade 1 with θ was analyzed as seen in Fig. 9 (a) and (b). The observed variation in Cm can be
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justified by looking at the flow around the blade at different θ. The major effect seen with the
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VAWT is the blade-vortex interactions in the downwind region.
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[Figure 9]
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It has been observed by Chandramouli et al. [22] that the torque experienced by each blade is
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similar for a given rotation except that they are phase shifted. Thus the torque experienced by
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blade 1 alone has been compared rather than combined torque. In Fig. 9 (a), the Cm peaks
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when the blade is near 180 degrees from the starting point for all three profiles. This indicates
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that the power generated by a blade during upwind is the maximum. NACA 0015 and NACA 9
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0030 profile during the downwind sweep is also significantly higher than the other two
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profiles, which explains the higher average Cp for NACA 0030 in the case of λ = 1.8. In Fig.
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9 (b), a trend similar to that observed in Fig. 9 (a) can be seen. It can be seen that NACA
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0015 attains maximum Cm while the Cm of all three profiles are almost identical in the
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downwind region.
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[Figure 10]
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A comparison of z-vorticity patterns at different sections along the NACA 0012 blades
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operating at λ = 1.8 is shown in Fig. 10. It can be observed that the contours at the symmetry
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plane and mid plane are almost identical while the one near the tip is different due to the
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blade tip interactions. Thus the z-vorticity seen at the symmetry plane extends for
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considerable length of the blade and therefore, the mid plane contours have been used to
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compare across the profiles.
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[Figure 11]
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The z-vorticity contours for 2 bladed NACA 0012 profile and NACA 0030 profile at low λ
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are shown in Fig. 11 (a) and (b) respectively at different azimuthal positions of blade 1. In the
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figure, θ = 0°-180° corresponds to the upwind of blade 1 and θ = 180°-360° corresponds to its
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downwind. Blade 1 at θ = 160° and θ = 180° in Fig. 11 (a) seems to have attached flow for a
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long duration indicating the maximum torque being generated. This has also been confirmed
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from Fig. 9 (a) that blade 1 generates maximum torque at around 180o. A strong vortex is
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seen on the inner side of the airfoil from 220°. As blade 1 moves further, it can be seen that
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the vortex grows, extending over a larger region leading to vortex shedding. This vortex
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shedding resulted in the reduction of the tangential force experienced by the blade and thus in
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lower power, as seen in Fig. 9 (a). In time, the shed vortex disappears due to interaction with
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free stream, and the cycle repeats. In the case of NACA 0030, a pattern similar to that
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observed for the NACA 0012 profile can be observed but the flow remained attached for a
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longer duration and vortex shedding is not seen at 220°, which is seen in the case of NACA
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0012. Thus the blade experiences a higher positive tangential force for a longer duration
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resulting in higher Cp. It can also be seen that the size of the vortex being shed is smaller in
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comparison. The vortex being shed dies down soon because of the weakening of the same
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due to the incoming free stream. All these results indicate that the performance of NACA
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0030 profile is better than NACA 0012 profile at λ = 1.8.
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At λ = 2.5, there is a reversal in performance with NACA 0015 performing better than NACA
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0030. The mid span z-vorticity contours of 2 bladed NACA 0015 profile and NACA 0030
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profile for λ = 2.5 is shown in Fig. 12 (a) and (b) respectively. The vortex shedding in NACA
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0015 starts much later as can be seen from the figures. Although the shed vortex does not die
296
down quickly, the interaction with the blade is not seen at all. The shed vortex moves
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downstream and away from the blade’s trajectory. This can be correlated to the higher Cp of
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NACA 0015. In the case of NACA 0030, the shed vortex seems smaller, however, there is
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some interaction with the blade in the downwind. The vortex being shed is dragged on for a
300
long duration causing some interaction between blade 1 and the vortex shed by blade 2. The
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power generated is maximum during the upwind sweep, similar to the observations made in
302
Fig. 11. Vortex generation starts just before 240°. The shed vortex does not die down soon
303
but it stays for a long while. These observations can be correlated to the decrease in Cp when
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compared to the observations made at λ = 1.8. It can also be observed that the Cp generated at
305
λ = 2.5 is comparable to the one generated by NACA0012 profile although the Cp of NACA
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0012 profile is slightly higher.
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The x-vorticity at the blade tip is looked into to understand its effect on the performance of
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VAWTs.
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[Figure 13]
Fig. 13 (a) and (b) shows the x-vorticity contours for various planes of NACA 0030 profile at
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λ = 2 and λ = 2.5 respectively. The plots were obtained to capture the tip vortex effects on the
312
flow of air around a VAWT. The z-vorticity plots below and very near the tip is not
313
significant and thus the x-vorticity is looked into. It can be seen that the tip vortex generation
314
and shedding starts at 160° and continues till 280°. The shed vortex from blade 1 interacts
315
with blade 2 for λ = 2.5 whereas there is minimal interaction with the vortex at λ = 2. Due to
316
this vortex interaction, Cp reduces for λ = 2.5. This shows the significant effect of tip vortex
317
on the performance of a VAWT. This clearly suggests that 3D simulations are necessary to
318
predict the performance of VAWTs efficiently, as seen in the validation study.
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[Figure 14]
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Fig. 14 (a) and (b) shows the variation of moment coefficient of the NACA 0012, NACA
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0015 and NACA 0030 with angle for λ = 1.8 and λ = 2.5 respectively. These follow the same 11
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pattern as observed in Fig. 9 (a) and (b) but the peaks are comparatively smaller. The
323
vorticity contours are looked into to correlate the flow characteristics to the torque
324
characteristics. [Figure 15]
326
The vorticity contours for 3 bladed NACA 0012 profile and NACA 0030 at low λ are shown
327
in Fig. 15 (a) and (b). NACA 0012 behaves similar to the observations made in Fig. 11.
328
Attached flow is predominant in the upwind region, where maximum Cp is generated. Vortex
329
shedding is observed to begin after 200°. The vortex shed by blade 3 interferes with blade 2
330
to a great extent, thereby affecting the torque experienced by blade 2. The free stream wind
331
does not suppress the shed vortex soon enough. In the case of NACA 0030, a trend similar to
332
NACA 0012 can be seen here. Blades in the upstream seem to have attached flows for a
333
longer duration. Vortex shedding starts much later compared to NACA 0012. Also, the size
334
of the vortex shed is small. The interaction between vortex shed by blade 3 and blade 2 is less
335
as the shed vortex dies down early.
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5.2 Effect of Solidity
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The effect of solidity is compared by changing the number of blades. Fig. 16 (a) and (b) show
339
a comparison of Cp for 2, 3 and 4 bladed NACA 0012 and NACA 0030 profiles respectively
340
with λ. The 3 bladed VAWT performs better at lower λ and the 2 bladed VAWT performs
341
better at higher λ in both cases and with increase of number of blades to 4, performance of
342
wind turbine deteriorates. The 2 bladed VAWT has a larger operating range and performs
343
best at λ = 2.8 as seen in the case of NACA 0012 where Cp = 0.332 and λ = 2 and in the case
344
of NACA 0030 where Cp = 0.35 as opposed to Cp = 0.253 at λ = 2.5 and 0.32 at λ = 1.8
345
respectively in the case of 3 bladed VAWTs.
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[Figure 17]
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At higher λ, 3 bladed turbines face higher interactions with the vortex, resulting in 2 bladed
349
turbines performing better, as shown in Fig. 17. However, we can see that at lower λ, the 3
350
bladed turbines perform better. This is because at higher solidity, the interception of blade
351
with the wind is more. Compared to the 2 bladed profiles, vortex generation is higher and
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therefore the vortex-blade interaction is also higher, resulting in lesser power generation
353
compared to 2 bladed turbines at high λ.
354
CONCLUSIONS
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Based on the observations made on the effect of airfoil profile and solidity on the
357
performance of VAWTs, the following conclusions were made.
358
1.
The validation study showed that 2D simulations overpredict the values of Cp at high λ. This is due to the inability of 2D models to capture 3D effects such as vortex interactions
360
and tip vortices. 2.
Among all the profiles compared, NACA 0030 attained maximum Cp for low tip speed
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ratios. Thicker airfoils performed better at low λ due to long durations of attached flow.
363
This resulted in faster vortex shedding and larger positive tangential force. As the λ was
364
increased, the Cp of NACA 0012 profile also increased. Thinner airfoils have larger
365
operating ranges than the thicker ones. This is because at larger λ, the shed vortex
366
dissipated much faster for thinner airfoils than for thicker airfoils, causing more vortex
367
interactions for thicker blades. Based on X vorticity contours, It was observed the tip
368
vortex generated interaction leads reduction in moment coefficient and hence, reduction
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in Cp.
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3. The Cp observed in 2 bladed VAWTs was higher than that of 3 bladed VAWT for a high
371
value of λ due to the increased occurrence of vortex interactions with the blades with
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higher solidity. However, at low λ, high solidity VAWTs performed better because the
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interaction of the blades with wind was better.
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Mertens, S., Wind energy in the built environment: concentrator effects of buildings. 2006: TU Delft, Delft University of Technology. Ferreira, C.S., G. van Bussel, and G. Van Kuik. 2D CFD simulation of dynamic stall on a vertical axis wind turbine: verification and validation with PIV measurements. in 45th AIAA aerospace sciences meeting and exhibit. 2007. Nevada, Reno. Hofemann, C., C. Simao Ferreira, G. Van Bussel, G. Van Kuik, F. Scarano, and K. Dixon. 3D Stereo PIV study of tip vortex evolution on a vawt. in The proceedings of the European Wind Energy Conference and exhibition EWEC, Brussels, 1-8. 2008. European Wind Energy Association EWEA. Stankovic, S., N. Campbell, and A. Harries, Urban wind energy. 2009: Earthscan.
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List of Figures
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Figure 1 H-Type Darrieus VAWT
435 436
Figure 2 Representation of Airfoil profiles – (a) NACA 0012; (b) NACA 0015; (c) NACA 0030; and (d) AIR 001
437 438
Figure 3 (a) 2D view of the domain; (b) 3D view of the meshed domains; (c) Fine mesh very close to the blade
439
Figure 4 Azimuthal angle, θ in (a) 2 bladed VAWT; and (b) 3 bladed VAWT
440
Figure 5 Variation of Cm with θ for 2 bladed NACA 0015 profile operating at λ = 1.3
441 442
Figure 6 (a) Time step independence and turbulence model independence; (b) grid independence
443
Figure 7 Benchmarking Studies
444
Figure 8 Variation of Cp with λ for (a) 2 bladed airfoil profiles; (b) 3 bladed airfoil profiles
445 446
Figure 9 Variation of moment coefficient of blade 1 with angle for 2 bladed profiles (a) at λ = 1.8; (b) at λ = 2.5
447 448
Figure 10 Comparison of z-vorticity patterns at different locations along the blade height for 2 bladed NACA 0012 at λ = 1.8
449 450
Figure 11 Mid span z-vorticity contours of 2 bladed (a) NACA 0012 profile; and (b) NACA 0030 profile at λ = 1.8
451 452
Figure 12 Mid span vorticity contours of 2 bladed (a) NACA 0015 profile; and (b) NACA 0030 profile at λ = 2.5
453 454
Figure 13 X – Vorticity contours of NACA 0030 profile at various angles for (a) λ = 2; and (b) λ = 2.5
455 456
Figure 14 Variation of moment coefficient with angle for 3 bladed airfoil profiles at (a) λ = 1.8; (b) λ = 2.5
457 458
Figure 15 Mid span vorticity contours of 3 bladed (a) NACA 0012 profile; and (b) NACA 0030 profile at λ = 1.8
459 460
Figure 16 Variation of Cp with λ for 2 bladed , 3 bladed and 4 bladed VAWT with (a) NACA 0012 airfoil; (b) NACA 0030 profile
461 462
Figure 17 Mid plane x-vorticity contours of (a) 2 bladed; and (b) 3 bladed NACA 0030 profiles operating at λ = 2.5
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Fig. 1 H-Type Darrieus VAWT 464
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(a)
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(b)
SC
(d) (c) Fig. 2 Representation of Airfoil profiles – (a) NACA 0012; (b) NACA 0015; (c) NACA 0030; and (d) AIR 001 466
AC C
EP
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467
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TE D
M AN U
(a)
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469
AC C
468
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(b) (c) Fig. 3 (a) 2D view of the domain; (b) 3D view of the meshed domains; (c) Fine mesh very close to the blade
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(a) (b) Fig. 4 Azimuthal angle, θ in (a) 2 bladed VAWT; and (b) 3 bladed VAWT
TE D
M AN U
SC
470
472
AC C
471
EP
Fig. 5 Variation of Cm with θ for 2 bladed NACA 0015 profile operating at λ = 1.3
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RI PT
473
EP
TE D
M AN U
SC
(a) (b) Fig. 6 (a) Time step independence and turbulence model independence; (b) grid independence
475 476
AC C
Fig. 7 Benchmarking Studies
474
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EP
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(a)
SC
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477 478
AC C
(b) Fig. 8 Variation of Cp with λ for (a) 2 bladed airfoil profiles; (b) 3 bladed airfoil profiles
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(a)
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479 480
AC C
(b) Fig. 9 Variation of moment coefficient of blade 1 with angle for 2 bladed profiles (a) at λ = 1.8; (b) at λ = 2.5
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180°
M AN U
SC
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Symmetric Plane (H/2)
AC C
Near Tip
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Quarter Plane (H/4)
Fig. 10 Comparison of z-vorticity patterns at different locations along the blade height for 2 bladed NACA 0012 at λ = 1.8
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SC
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481
160°
EP
TE D
M AN U
160°
180°
AC C
180°
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ACCEPTED MANUSCRIPT 220°
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220°
260°
AC C
EP
300° (a)
TE D
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260°
300° (b)
Fig. 11 Mid span z-vorticity contours of 2 bladed (a) NACA 0012 profile; and (b) NACA 0030 profile at λ = 1.8 482 483
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160°
200°
AC C
EP
200°
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160°
240°
240°
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280°
EP
320° (a)
TE D
M AN U
280°
320° (b)
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AC C
Fig. 12 Mid span vorticity contours of 2 bladed (a) NACA 0015 profile; and (b) NACA 0030 profile at λ = 2.5
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40°
160°
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160°
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SC
40°
280°
280°
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M AN U
486 487
360° 360° (b) (a) Fig. 13 X – Vorticity contours of NACA 0030 profile at various angles for (a) λ = 2; and (b) λ = 2.5
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488
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(a)
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AC C
(b) Fig. 14 Variation of moment coefficient with angle for 3 bladed airfoil profiles at (a) λ = 1.8; (b) λ = 2.5
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491
160°
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160°
200°
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200°
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240°
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240°
280°
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280°
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320°
320° (b)
M AN U
(a)
Fig. 15 Mid span vorticity contours of 3 bladed (a) NACA 0012 profile; and (b) NACA 0030 profile at λ = 1.8
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(a) NACA 0012
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AC C
(b) NACA 0030 Fig. 16 Variation of Cp with λ for 2 bladed, 3 bladed and 4 bladed VAWT with (a) NACA 0012 airfoil; (b) NACA 0030 profile
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496
200°
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200°
240°
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240°
280°
280° 35
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320° (b)
M AN U
320° (a)
Fig. 17 Mid plane x-vorticity contours of (a) 2 bladed; and (b) 3 bladed NACA 0030 profiles operating at λ = 2.5 497
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498
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ACCEPTED MANUSCRIPT Table 1 – Details of the Turbine NACA 0015
Chord, c
0.420 m
Diameter of rotor
2.7 m
Frontal area of rotor
8.1 m2
Solidity, σ
0.33, 0.5
Number of blades
2, 3
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Blade profile
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3D simulations account for tip vortices and thus predicts more realistically. Thicker airfoils perform better at lower TSR Thinner airfoils have wider range of operational TSR
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Higher solidity performs better at lower TSR