Design and Performance of a Straight-Bladed Darrieus Wind Turbine

Transcription

1 International Journal of Applied Engineering Research, ISSN Vol. 10 No.5 (015) pp Design and Performance of a Straight-Bladed Darrieus Wind Turbine S. Brusca Researcher Department of Electronic Engineering, Chemical and Industrial Engineering, University of Messina sbrusca@unime.it R. Lanzafame Full Professor Department of Industrial Engineering, University of Catania rlanzafa@dii.unict.it M. Messina Full Professor Department of Industrial Engineering, University of Catania mmessina@dii.unict.it Abstract-In this paper a procedure to maximize the energy production and power coefficient of a Vertical Axis Wind Turbine with straight blades is presented. The Multiple Stream Tube Model was used to predict the performance of the Vertical Axis Wind Turbine with straight blades and five different symmetric airfoils were compared. In particular, NACA 001, NACA 0015, NACA 0018, NACA 001 and NACA 005 were tested. For each considered airfoil and for specific rotor solidity and tip speed ratio maximum wind turbine power coefficient was obtained. Moreover, a methodology for achieving the maximum extracted energy at each wind velocity is presented. Finally, on the basis of the presented results it is possible to conclude that maximum energy production and maximum power coefficient can be achieved using a wind turbine rotor with only two blades. Keywords: VAWT, MSTM, NACA Airfoils, Power Coefficient. Introduction Nowadays, fast growing of energy demand and stringent regulation about pollution lead to a necessary increase of energy sources as well as diversification [1]. Non-conventional fuels could represent a good strategy for source diversification [ 4], while renewables meet both increase of energy sources and diversification. Among renewable energy sources wind power plays certainly an important role [1]. Therefore, several authors spend a lot of efforts to optimize wind turbines [5 8] and wind systems [9, 10]. In the field of power generation from wind source two types of wind turbines are mainly used: Horizontal Axis Wind Turbines (HAWTs) and Vertical Axis Wind Turbines (VAWTs). In general the latter, and VAWTs with straight blades in particular, are the simplest. In fact, this type of turbines has a simplified geometry with no yaw mechanism or pitch regulation, and have neither twisted nor tapered blades [11]. VAWTs are mainly used in power generation but several others applications are possible (e.g. water pumping) [11]. Furthermore, VAWTs can handle the wind from any direction regardless of orientation and are inexpensive and produce low noise [1]. Wind turbines have aroused the interest of both industry and the academic community [13 4, 33 35]. Several authors studied advantages and drawbacks of the two wind turbines main types (VAWT and HAWT) comparing different wind turbines from the most important aspects including structural dynamics, control systems, maintenance, manufacturing and electrical equipment [13 14]. Taking into account the positioning of wind turbine, turbulence [15], obstacle [16 17] and turbine mutual influence on energy conversion [10], it is highly important to study the wind characteristics in off-shore, inland and urban wind turbine position [15]. Several authors highlighted the influence of turbulence over urban-type roughness [16 17] as well as over offshore installations [19]. Therefore, several numerical codes for designing and evaluating wind rotor performance were implemented. Recent studies [5 35] have highlighted that VAWTs can achieve significant improvements in efficiency by means of rotor design [5 8], airfoil studies [31], blade optimization in wind tunnels [3 34], influence on wind turbine performance of constitutive parameters such as aspect ratio [7]. In the present paper, a numerical code based on the Multiple Stream Tube Model (MSTM) applied to five different symmetrical airfoils was implemented and optimal configurations were set up to achieve high power coefficients. Moreover, a new methodology for achieving maximum energy production and maximum power coefficient is presented. Nomenclature a Interference factor [-] V 0 Free stream wind speed [m/s] V Reduced wind speed [m/s] R Rotor radius [m] w Rotor angular velocity [s -1 ] h Blade length [m] ω Airfoil relative wind speed [m/s] α Angle of attack [ ] L Lift [N] D Drag [N] R* Resultant force [N] ϑ Blade angular position [ ] Rotor power [W] P T Rotor Torque [Nm] N b Number of blades [-] T(ϑ) Instantaneous torque [Nm] F T (ϑ) Instantaneous tangential force [N]

2 International Journal of Applied Engineering Research, ISSN Vol. 10 No.5 (015) ρ Air density [kg/m 3 ] C T Tangential force coefficient [-] c Airfoil chord [m] C L Lift coefficient [-] C D Drag coefficient [-] c p (ϑ) Local power coefficient [-] c p Power coefficient [-] A Rotor frontal area [m ] λ Tip speed ratio [-] Re Reynolds Number [-] P(ϑ) Local Power [W] σ Rotor solidity [-] σ cpmax σ that maximizes the c p [-] λ cpmax λ that maximizes the c p [-] c pmax Maximum value of the c p [-] n Rotor rotational velocity [r/min] C N Axial force coefficient [-] Fig.1. Vertical Axis Wind Turbine, H-Type from [11] Abbreviations NACA National Advisory Committee for Aeronautics VAWT Vertical Axis Wind Turbine HAWT Horizontal Axis Wind Turbine TSR Tip Speed Ratio Aerodynamic Model The numerical code is based on the theory developed by Strickland [30], which is based on Glauerts Blade Element Momentum Theory [31] utilizing the stream wise momentum equation in conjunction with the aerodynamic forces acting on the rotor blades. Numerical computations are performed for a series of stream tubes which pass through the rotor, varying the rotational angle ϑ from 0 to 180, and considering rotor performances in the downwind region (180 ϑ 360 ) as the same as those in the upwind region (0 ϑ 180 ). By calculating the equation of momentum for each stream tube with the aerodynamic forces acting on the blade, it is possible to create an iterative procedure (as reported in [30]) for correctly determining the interference factor a (Eq. 1) and so on for the torque and power (strongly influenced by the interference factor). In Eq. 1, a is defined as: a = (1) V 1 V 0 V = V 1 0 Wind velocity V near the blade is: ( a) V being the reduced wind velocity near the blade, and V 0 the far upstream wind velocity. With the notation adopted in Fig.1 and Fig., wind rotor power can be calculated (see Eq. 3 8). () Fig.. Wind rotor rotational plane Mean wind rotor power is reported in Eq. 3. P = T ω (3) where T is the mean value of instantaneous torque T(ϑ) multiplied by the number of blades N b : T = T ( ϑ ) N b. Instantaneous torque (T (ϑ)) can be evaluated if the instantaneous tangential force F T (ϑ) is known. T ( ϑ ) = F T ( ϑ ) R (4) Instantaneous tangential force is a function of relative wind speed w (see Fig.), tangential force coefficient C T, airfoil chord c and blade length h. 3980

3 International Journal of Applied Engineering Research, ISSN Vol. 10 No.5 (015) FT (ϑ ) = 1 ρ CT (ϑ ) w (ϑ ) c h (5) Having selected the airfoil blade, the tangential force coefficient can be calculated from the tabulated values of lift and drag coefficients and the airfoil s angle of attack. CT (ϑ ) = CL (ϑ ) sin α (ϑ ) CD (ϑ )cosα (ϑ ) (6) Relative wind speed is reported in Eq. 7, and the angle of attack is reported in Eq. 8 (see Fig. for calculating w and α ). w (ϑ ) = "#ω R +V0 (1 a (ϑ )) cosϑ $% + +"#V0 (1 a (ϑ )) sin ϑ $% (7) Fig.3. Angular sector Δϑ for each stream tube (a) V0 (1 a(ϑ )) sin ϑ α (ϑ ) = arctan ωr + V0 (1 a(ϑ ))cos ϑ (8) For each value of ϑ, all the mathematical expressions (Eq. 3 8) are functions of the unknown a. In [30], Strickland developed an iterative procedure for evaluating a based upon two calculations of the stream tube force: one with the equation of momentum conservation, and another with the equation of the aerodynamic forces. Equating these two equations, the a value can be obtained and applied within the iterative loop. Wind Rotor Design at Maximum Efficiency The power coefficient (cp) for a wind rotor is the mean value of the instantaneous power coefficient cp(ϑ) which is defined in Eq. 9: c p (ϑ ) = where (b) P(ϑ ) 1 ρ AV03 P (ϑ ) = T (ϑ ) ω N b (9), A being the stream tube cross- A = R Δϑ sin ϑ h, and Δϑ being the sectional area defined as related angular sector for each stream tube (see Fig.3). Each of the five airfoils had the numerical code based on the Multiple Stream Tube Model applied to them. Each (see Fig. 4) power coefficient was calculated as a function of the Tip Speed Ratio (λ) and rotor solidity (Eq. 10). The lift and drag coefficients for the five airfoils were calculated with Re = 106 [3]. As shown in Fig.4, there is a rotor solidity value (at a particular TSR) for each airfoil, which maximizes the power coefficient. Table 1 reports the values that maximize the power coefficients. 3981

4 International Journal of Applied Engineering Research, ISSN Vol. 10 No.5 (015) (c) As shown in Fig.4 and Table 1, the NACA 0018 and NACA 005 airfoils have the highest power coefficients being greater than 0.5. TABLE.1. Power coefficients of the five airfoils Airfoil NACA 001 NACA 0015 NACA 0018 NACA 001 NACA 005 σcpmax λcpmax cpmax Rotor solidity is defined in Eq. 10. N c σ= b R (10) From Eq. 10, the number of blades (Nb) can be calculated, as a function of c/r and solidity, which maximizes the power coefficient (Eq. 11). (d) Nb = σ cp max c R (11) For all five airfoils, the Nb trend as a function of c/r ratio is reported in Fig.5. Each curve is characterized by a constant value of solidity and cp (cp = cpmax; σ = σcpmax). Once the airfoil (obviously one of those which have the higher cp), in Fig.5 is chosen, notice how the maximum cp value can be achieved independently of the number of blades. In other words, considering for example NACA 0018, it is possible to design a wind rotor with two blades and c/r = 0., or three blades and c/r = 0.133, or four or five blades, etc., all with cp = cpmax = Once the wind rotor power coefficient has been maximized, the height of the blade and the rotor radius must be chosen to obtain the desired power. Alternatively to the expression reported in Eq. 3, the wind rotor power can be written as in Eq. 1, where A = R h and V0 is the free stream wind velocity (the higher cp, the smaller area A is). (e) P= 1 ρ c p AV03 (1) In Fig.5, only two curves have the maximum cp (curve (b) - NACA 0018; curve (c) - NACA 005). As stated earlier, maximum cp can be achieved with only two blades: airfoil NACA 0018, c/r = 0.; airfoil NACA 005, c/r = 0.5. Fig.4. Rotor solidity effect on power coefficient 398

5 International Journal of Applied Engineering Research, ISSN Vol. 10 No.5 (015) NACA 005 airfoil is shown with c p = c pmax = 0.51, σ = 0.5 and λ =.. In Fig.7, notice how increasing the rotor radius decreases the wind rotor rotational velocity. Fig.5. Wind rotor design charts In Fig.5, only two curves have the maximum c p (curve (b) - NACA 0018; curve (c) - NACA 005). As stated earlier, maximum c p can be achieved with only two blades: airfoil NACA 0018, c/r = 0.; airfoil NACA 005, c/r = 0.5. In Fig.3, notice that the maximum c p is related to a specific rotor solidity, and also to a specific Tip Speed Ratio. The c p is maximized when σ = σ cpmax and λ = λ cpmax (see Table 1). The Tip Speed ratio is defined as: λ = ω R / V 0. When λ = λ cpmax then: n R = 60 π λ cpmax V 0 (13) where n is the rotational velocity expressed in [rpm]. VAWT operating at varying rotational velocities When V 0 varies, the parameter n R must vary linearly to achieve the maximum c p value for any V 0 (see Fig.6). Fig.7. Wind rotor rotational velocity varying with wind speed variations for different rotor radii Concluding, it is advisable to adopt the NACA 005 airfoil for designing a micro or mini VAWT, with its lower rotational velocity and greater chord (insignificant for small turbines). By contrast, it is advisable to adopt the NACA 0018 airfoil to design a larger VAWT: greater velocity of rotation (insignificant because as rotor radius increases, the curve slope decreases), and smaller chord (economic advantage). By controlling the wind rotor rotational velocity as wind speed varies, the maximum c p value can always be obtained. Fig. 8 shows the case for a -bladed wind turbine with R = 5 m, the NACA 005 airfoil with σ = 0.51 and λ =.. Fig.6. n R trend versus wind speed The NACA 0018 curve has the greater slope compared to NACA 005 airfoil (both with c p = 0.51). This fact means that for any wind speed V 0, the rotational velocity of the NACA 005 wind turbine will be smaller. The chart in Fig.6 can be parameterized with the rotor radius. In Fig.7, the case for the Fig.8. VAWT at variable rotational velocity Aerodynamic analysis for the optimized wind turbine 3983

6 International Journal of Applied Engineering Research, ISSN Vol. 10 No.5 (015) This case study has considered an optimized wind rotor with a power coefficient of 0.51, a rotor radius of 5 m, the two straight blades of the NACA 005 airfoil, a chord of 1.5 m, a rotor solidity of 0.5 and a tip speed ratio of.. The aerodynamic characteristics for the optimized wind rotor are shown in Fig.9. Fig.9a reports the airfoil angle of attack versus the rotor rotational angle ϑ. The maximum value of the angle of attack is about 18.7 at ϑ = 118.4, and the flow is always in the attached flow region. The interference factor a is always positive (see Fig.9b), the maximum value (a = 0.379) is reached for ϑ = 80, while the minimum values were ϑ = 0 and ϑ = 180. With the graph in Fig. 9c showing the normal force coefficient CN, the force at right angles to the axis of rotation can be calculated. Finally, Fig.9e shows the normalized value of the airfoil s relative velocity. Its maximum value is ϑ = 0 and the minimum value is ϑ = 180. The trend of the relative velocity w must be calculated to evaluate the Reynolds number, and therefore the corresponding CL and CD tables. (c) (d) (a) (e) (b) Fig.9. Aerodynamic characteristics for the optimized wind rotor Conclusion The present work has investigated the performances of vertical axis wind turbines with straight blades. A new strategy to maximize VAWT performances was evaluated and applied. Five different symmetrical airfoils were tested to highlight their relative performances. A series of parametric graphs were drawn to evaluate the rotor solidity, which maximizes the power coefficient, and other parametric graphs 3984

7 International Journal of Applied Engineering Research, ISSN Vol. 10 No.5 (015) to design the rotor blades to maximum efficiency. Having the highest efficiency airfoil, the blade chord that provides maximum rotor efficiency with only two blades can be chosen. A third series of parametric graphs were drawn to evaluate the link between wind rotor rotational velocity and the variation in free stream wind velocity. In this way, the wind rotor will always work at the maximum power coefficient, even if the free stream wind velocity varies. Different design strategies were highlighted for mini VAWTs and larger VAWTs with high efficiency and only two blades. For the former, it is advisable to choose airfoils with larger chords and lower rotational velocities, and for the latter, the opposite design strategy is advisable. Finally, a case study was developed for a wind turbine with a rotor solidity of 0.5 and a Tip Speed Ratio of. for which the performances were evaluated, the airfoil was chosen, and the aerodynamic characteristics were highlighted. In conclusion, even though the mathematical model (MSTM) applied is the simplest of those in the scientific literature, this methodology evaluates the performances of different aerodynamic airfoils and provides the data needed to design a VAWT with a high power coefficient and only two blades. The model simplicity leads to high computer running performance that makes the MSTM suitable to be used as objective function in optimization algorithms. In future research, a mathematical model based on a Double MSTM will be applied to better predict when VAWTs are simulated. References [1] IEA (International Energy Agency). World Energy Outlook, OECD/IEA, 013. [] S. Brusca, V. Chiodo, A. Galvagno, R. Lanzafame, A. Marino Cugno Garrano. Analysis of reforming gas combustion in Internal Combustion Engines, Energy Procedia, vol. 45, pp , 014. [3] S. Brusca, R. Lanzafame, A. Marino Cugno Garrano, M. Messina. On the possibility to run an Internal Combustion Engine on acetylene and alcohol, Energy Procedia, vol. 45, pp , 014. [4] S. Brusca, A. Galvagno, R. Lanzafame, A. Marino Cugno Garrano, M. Messina. Performance Analysis of Biofuel Fed Gas Turbine, 69th ATI National Congress, September, Milan, Italy, 014. [5] A. Bianchini, G. Ferrara, L. Ferrari. Design guidelines for H- Darrieus wind turbines: Optimization of the annual energy yield, Energy Conversion and Management, vol. 89, pp , 015. [6] A. Chehouri, R. Younes, A. Ilinca, J. Perron, Review of performance optimization techniques applied to wind turbines, Applied Energy, vol. 14, pp , 015. [7] S. Brusca, R. Lanzafame, M. Messina. Design of verticalaxis wind turbine: how the aspect ratio affects the turbine s performance, International Journal of Energy and Environmental Engineering, vol. 5, pp , 014. [8] S. Brusca, R. Lanzafame, M. Messina. Flow similitude laws applied to wind turbines through blade element momentum theory numerical code, International Journal of Energy and Environmental Engineering, vol. 5, pp , 014. [9] S. Rajper, I.J. Amin. Optimization of wind turbine micrositing: A comparative study, Renewable and Sustainable Energy Reviews, vol. 16, pp , 01. [10] S. Brusca, R. Lanzafame, M. Messina. Wind turbine placement optimization by means of the Monte Carlo simulation method, Modeling and Simulation in Engineering, vol. 014, pp. 1-8, 014. [11] M. Islam, D.S.K. Ting, A. Fartaj. Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines, Renewable and Sustainable Energy Reviews, vol. 1, pp , 008. [1] K. Pope, G.F. Naterer, I. Dincer, E. Tsang. Power correlation for vertical axis wind turbines with varying geometries, International Journal of Energy Research, vol. 35, pp , 011. [13] S. Eriksson, H. Bernhoff, M. Leijon. Evaluation of different turbine concepts for wind power, Renewable and Sustainable Energy Reviews, vol. 1, pp , 008. [14] H. Riegler. HAWT versus VAWT: small VAWTs find a clear niche, Refocus, pp , 003. [15] J. Rohatgi, G. Barbezier. Wind turbulence and atmospheric stability their effect on wind turbine output, Renewable Energy, vol. 16, pp , [16] I.P. Castro, H. Cheng, R. Reynolds. Turbulence over urban-type roughness: deductions from wind-tunnel measurements, Boundary-Layer Meteorology, vol. 118, pp , 006. [17] Y.A. Gayev, E. Savory. Influence of street obstructions on flow processes within urban canyons, Journal of Wind Engineering and Industrial Aerodynamics, vol. 8, pp , [18] V. Akhmatov. Influence of wind direction on intense power fluctuations in large offshore wind farms in the North Sea, Wind Engineering, vol. 31(1), pp , 007. [19] A.D. Sahin, I. Dincer, M.A. Rosen. Thermodynamic analysis of wind energy, International Journal of Energy Research, vol. 30, pp , 006. [0] A.K. Wright, D.H. Wood. The starting and low wind speed behavior of a small horizontal axis wind turbine, Journal of Wind Engineering and Industrial Aerodynamics, vol. 9, pp ,

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