Design of a vertical-axis wind turbine: how the aspect ratio affects the turbine’s performance

S. Brusca 0 1 R. Lanzafame 0 1 M. Messina 0 1 0 R. Lanzafame M. Messina (&) Department of Industrial Engineering, University of Catania , Viale A. Doria, 6, 95125 Catania, Italy 1 S. Brusca Department of Electronic Engineering, Chemical and Industrial Engineering, University of Messina , Contrada Di Dio, 98166 Messina, Italy This work analyses the link between the aspect ratio of a vertical-axis straight-bladed (H-Rotor) wind turbine and its performance (power coefficient). The aspect ratio of this particular wind turbine is defined as the ratio between blade length and rotor radius. Since the aspect ratio variations of a vertical-axis wind turbine cause Reynolds number variations, any changes in the power coefficient can also be studied to derive how aspect ratio variations affect turbine performance. Using a calculation code based on the Multiple Stream Tube Model, symmetrical straight-bladed wind turbine performance was evaluated as aspect ratio varied. This numerical analysis highlighted how turbine performance is strongly influenced by the Reynolds number of the rotor blade. From a geometrical point of view, as aspect ratio falls, the Reynolds number rises which improves wind turbine performance. - Abbreviations NACA National Advisory Committee for Aeronautics VAWT Vertical-axis wind turbine H-Rotor VAWT with straight blades TSR Tip speed ratio MSTM Multiple Stream Tube Model AR Aspect ratio This paper evaluates VAWT performance; How Reynolds number influences rotor performance has been studied; How Reynolds number is linked to rotor aspect ratio has been investigated; A new design procedure governing the rotors aspect ratio has been presented; The new design procedure maximizes wind turbine efficiency. chosen empirically on the basis of the experience of the designer, and not on scientific considerations. In this work, the link between the aspect ratio of a wind turbine and its performance has been studied, and a correlation between the aspect ratio and the turbines performance has been found. There are two types of wind turbine which produce electrical energy from the wind: they are horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs). The second, and in particular straight-bladed VAWTs, have a simplified geometry with no yaw mechanism or pitch regulation, and have neither twisted nor tapered blades [1]. VAWTs may be utilized to generate electricity and pump water, as well as in many other applications [1]. Furthermore, they can handle the wind from any direction regardless of orientation and are inexpensive and quiet [2]. Wind turbines have aroused the interest of both industry and the academic community [315, 2931], which have developed different numerical codes for designing and evaluating wind rotor performance. Recent studies [1620] have highlighted that VAWTs can achieve significant improvements in efficiency. VAWT can work even when the wind is very unstable making them suitable for urban and small-scale applications [21]. Their particular axial symmetry means they can obtain energy where there is high turbulence. Their optimum operating conditions (maximum power coefficient) depend on rotor solidity and tip speed ratio [22]. For a VAWT rotor solidity depends on the number of blades, airfoil chord and rotor radius. Tip speed ratio is a function of angular velocity, undisturbed wind speed and rotor radius. In the design process of a vertical-axis wind turbine it is crucial to maximize the aerodynamic performance [22, 26]. The aim is to maximize the annual energy production by optimizing the curve of the power coefficient varying with the tip speed ratio [25]. For a fixed cross-sectional area of the turbine, to optimize the curve of the power coefficient it is possible to use different airfoil sections and/or rotors with different solidity [26]. To maximize energy extraction, other authors introduced guide vanes [27] and/or blade with a variable pitch angle [28] in vertical-axis wind turbines. In the design process of a vertical-axis wind turbine, a wrong choice of the aspect ratio of the wind turbine may cause a low value of the power coefficient (wind turbine efficiency). This parameter (the aspect ratio) is often Fig. 1 Power coefficient for a VAWT, straight blades and symmetric airfoil Designing an H-Rotor Designing a vertical-axis wind turbine with straight blades requires plotting power coefficient cp against tip speed ratio k, as a function of rotor solidity r (Fig. 1). Figure 1 shows the behaviour of the power coefficient for a wind turbine with straight blades and a NACA 0018 airfoil. Figure 1 curves were obtained using a calculation code based on MSTM theory [23]. From the graph in Fig. 1, the solidity which maximizes power coefficient r = 0.3 can be identified, which has a cpmax = 0.51 corresponding to k = 3.0. Since solidity r equals: chord c can be expressed as a function of solidity, rotor radius and blade number Nb, as per Eq. 2: The power of a wind turbine with a vertical axis can be expressed as per Eq. 3: Having defined the turbines aspect ratio (AR) as the ratio between blade height and rotor radius (AR = h/R), rotor radius can be derived from Eq. 3: (in Eq. 4 power P and wind velocity V0 are design data and q is air volume mass). This design approach is iterative and from time to time it will be necessary to re-evaluate the blades Reynolds number and if necessary repeat the procedure with new power coefficient curves. The local Reynolds number is: c w Re m 5 where c is the chord from Eq. 2, m is the kinematic air viscosity, and w is the air speed relative to the airfoil as Fig. 2 shows. Adopting a mathematical approximation, to evaluate the Reynolds number, w can be substituted by xR with the advantage of having a mean Reynolds number independent of the angle # of rotation (see Fig. 2). To conclude the design cycle, simply calculate xR directly from TSR relative to cpmax identifiable in Fig. 1, and combining Eqs. 5 and 6: If the Reynolds number thus calculated is different to the one for the power coefficient curve adopted initially (Fig. 1), a new power coefficient curve should be plotted for a different Reynolds number (second attempt). Usually, the iterative design process needs only 2 or 3 iterations. Figure 3 shows the power coefficient curves for the wind turbine with the NACA 0018 airfoil, at high Reynolds numbers. Fig. 3 Characteristic curves for high Reynolds numbers Fig. 4 Effect of aspect ratio (h/R) on VAWT performance In conclusion, the Reynolds number strongly influences the power coefficient of a vertical-axis wind turbine. Furthermore, it changes as the main dimensions of the turbine rotor change. Increasing rotor diameter rises the Reynolds number of the blade. The importance of aspect ratio In Eq. 4 note how radius R increases as ratio AR decreases. In Eq. 2 if R increases, chord c increases too, and in Eq. 7 note how increasing the chord rises the Reynolds number. (...truncated)