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The aerodynamics of a camber-bladed vertical axis wind turbine in unsteady wind Michael D. Bausas a, Louis Angelo M. Danao a, b, * a b

Energy Engineering Program, University of the Philippines, Diliman, Quezon City, Philippines Department of Mechanical Engineering, University of the Philippines, Diliman, Quezon City, Philippines

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 March 2015 Received in revised form 25 September 2015 Accepted 27 September 2015 Available online xxx

VAWT (Vertical axis wind turbines) pose several advantages over the horizontal axis machines that make them more suitable for applications where wind conditions are inherently turbulent. However, due to the complexity of VAWT aerodynamics, technical literature on the subject is very limited with research on VAWT performance mostly focused on steady wind analysis. This paper aims to numerically predict the performance of a 5 kW VAWT under ﬂuctuating wind conditions through computational ﬂuid dynamics modeling. Two dimensional VAWT models using symmetric and cambered blades were created with open ﬁeld boundary extents. Fluctuating wind speed was imposed on the inlet with average magnitude of 5 m/s, amplitude of ﬂuctuation of 10%, and frequency of ﬂuctuation of 1 Hz. Results revealed that ﬂuctuating wind imposes a detrimental effect on VAWT performance. A VAWT blade with 1.5% camber shows the best performance with the cycle-averaged unsteady power coefﬁcient at 0.31 versus the optimum steady power coefﬁcient of 0.34. In spite of increased available wind power due to the ﬂuctuating wind at 233.13 Watts in one wind cycle compared to 229.69 Watts for the steady 5 m/s wind case, power generated by the camber bladed VAWT drops to 74.96 Watts from the steady wind rotor power of 78.32 Watts. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Camber CFD NACA Unsteady wind VAWT

1. Introduction In the wind power domain, most research and development work is focused on HAWTs (horizontal axis wind turbines), making it a more mature wind technology than VAWTs (vertical axis wind turbines). HAWTs are more efﬁcient than VAWTs but essentially require laminar wind ﬂow or good quality wind energy [1,2]. Results from previous studies, on the other hand, have shown that VAWTs are theoretically more suitable for small scale power generation in urban terrain, where wind conditions are turbulent rather than steady [2,3]. There are several advantages of VAWTs over HAWTs that make them preferable for such conditions, namely: ability to accept wind from any direction eliminating the need of a yaw control system; performance is less affected by turbulent wind ﬂow; compact and simple in design as some mechanical components can be situated at the base of the turbine,

* Corresponding author. Department of Mechanical Engineering, University of the Philippines, Diliman, Quezon City, Philippines. Tel.: þ63 29818500x3130; fax: þ63 29208860. E-mail address: [email protected] (L.A.M. Danao). http://dx.doi.org/10.1016/j.energy.2015.09.120 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

alleviating material stress on the tower; and maximum power coefﬁcient (CP) is achieved at low tip speed ratios (l), thus reducing noise and safety hazards. Despite having the same order of CP and numerous advantages over HAWT, VAWT still requires proper technology research and development to improve self-starting and optimize wind power extraction. A number of parameters still need to be optimized, such as l, solidity, blade number, blade shape and, camber as well as constant or variable blade pitch offset [4]. However, due to the difﬁculty and complexity of modeling VAWT aerodynamics, related technical studies are scarce in literature which mostly deal with experimental and numerical analysis of VAWT performance under steady wind conditions [5]. The focus of this paper is to investigate the effect of blade camber on the overall performance of VAWT that is subjected to changing wind speeds. To do so, two dimensional ﬂow ﬁeld around the VAWT was numerically simulated and analyzed through CFD (computational ﬂuid dynamics) modeling. Results from the unsteady wind simulations, such as ﬂow ﬁeld characteristics, torque, power and power coefﬁcient variations, as well as lift and drag over one complete wind cycle were compared between said VAWT proﬁle and its symmetric-bladed counterpart.

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Nomenclature c blade chord Cd drag coefﬁcient Cl lift coefﬁcient CP power coefﬁcient Dg gust length fc characteristic frequency of unsteady wind kgust reduced gust frequency keu SST variant of keu turbulence model by Menter (1993) nrev number of revolutions per wind cycle PB blade power (three blades) Pw wind power R rotor radius Tb blade torque (single blade) TB blade torque (three blades) U∞ free stream wind speed

1.1. Effect of unsteady wind on the performance of various VAWT designs With the recent development of computing machines and software technology, accurate modeling of the unsteady wind performance of VAWTs has become more achievable. Below are some related studies that have been conducted to gain better understanding of the ﬂow ﬁelds around a VAWT in unsteady wind conditions. McIntosh et al. [6] tested the performance of a VAWT that rotates at a constant speed under sinusoidal wind condition. Their results revealed that energy extraction is increased when using a rotational speed greater than that of the steady state maximum. They used an over-speed control technique that translates into a 245% energy yield increase. Moreover, their results suggest that an additional 42% increase in energy extraction can be achieved when a tip speed ratio feedback controller that incorporates time dependent effects of gust frequency and turbine inertia is used. The generated unsteady CP curve closely tracks that of the steady CP at low ﬂuctuation frequencies (0.05 Hz) and forms hysteresis loops at higher ﬂuctuation frequencies (0.5 Hz) that averages higher than steady results. Iida et al. [7] also studied the performance of a straight-bladed VAWT with three airfoils under unsteady wind ﬂow using Large Eddy Simulation. They validated their results with those derived from momentum theory and showed good agreement at high tip speed ratio. On the other hand, at low tip speed ratio, high variation were observed from the predicted torque coefﬁcients of the two models. This variation is said to occur due to the dynamic stall effect. 2D and 3D simulations of a rooftop-sized H-type VAWT were conducted by Hamada et al. [8]. Results from the 2D simulation showed high variations in lift coefﬁcients from the downwind and upwind side of rotation with low power extraction on the downwind side. A different dynamic behavior was observed for the VAWT blades under study compared to that of a pitching blade as inﬂuenced by the variation of both the direction and magnitude of relative incoming velocity. The maximum torque for the revolution was computed at an azimuth angle beyond blade stall. Blade tip vortices and support arm drag proﬁles were revealed during 3D simulation which subsequently resulted to signiﬁcantly lower wind power yield. Mertens and Van Bussel [3] also studied a roof H-Darrieus type VAWT subjected in skewed ﬂow. Their results were validated with a

Uamp Umean yþ

a DCP q l lmean mf u umean CFD DMS HAWT LES RANS VAWT

amplitude of ﬂuctuation of unsteady wind mean speed of unsteady wind dimensionless wall distance angle of attack change in CP azimuth position tip speed ratio, Ru/U∞ tip speed ratio corresponding to umean dynamic viscosity of ﬂuid Instantaneous rotor angular speed mean of u Computational Fluid Dynamics double multiple streamtube model horizontal axis wind turbine large eddy simulation Reynolds averaged NaviereStokes vertical axis wind turbine

Blade Element Momentum model where better performance of VAWT in skewed ﬂow was showed. The study suggests that the HDarrieus VAWT is more suited for application on ﬂat roofs of high structures as compared to HAWT. Unsteady wind simulation of micro VAWT with blade design combining rotating movement around each blade axis and the and Bois [9]. Results nacelle's was conducted by Bayeul-Laine showed very good performance of the VAWT due to the minimal inﬂuence of each blade to the ﬂow stream around the next blade so thus on power yield. The maximum mean power coefﬁcient is computed to be 0.32. Scheurich and Brown [5] investigated the performance of three different VAWT conﬁgurations: straight-bladed, curved-bladed and helically twisted blades using vorticity transport model. Results showed that at constant rotational speed, in unsteady wind, the most efﬁcient VAWT conﬁguration is the one with helically twisted blades. The power loss experienced by the non-twisted blades are higher because they have variation of CP with tip speed ratio that exhibits steeper gradient in mid-operating range than the turbine with helically twisted blades. In steady wind conditions, the power coefﬁcients that are produced by both the straight-bladed and curved-bladed turbines vary considerably within one rotor revolution because of the continuously varying angle of attack on the blades and, thus, the inherent unsteadiness in the blade aerodynamic loading. These variations are much larger, and thus far more signiﬁcant, than those that are induced by the unsteadiness in the wind conditions. Wang et al. [10] carried out a 2D numerical simulation of the unsteady ﬂow ﬁeld over a VAWT using RANS equations. Results showed that the velocity magnitude in the region of wind turbine's rotation was much higher than the air ﬂow of the upstream, the eddy is much larger in the upper blade's back of the wind turbine's rotational part, while eddy is less in the lower blade's back of the wind turbine's rotational part; and at the same rotational speed, the condition of lower wind velocity has larger total torque coefﬁcient at the same rotational speed. Danao et al. [11] conducted both experimental and numerical investigations of the effect of unsteady wind on the aerodynamic performance of straight-bladed vertical axis wind turbine. Results of their study showed that periodically changing wind conditions can slightly improve the overall performance of VAWT when certain conditions are satisﬁed, such as: the mean tip speed ratio is just above the l of the steady CP maximum, the amplitude of

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ﬂuctuation is small, and the frequency of ﬂuctuation is high. Operation outside these deﬁned conditions may cause the VAWT to run in l bands with deep stall and vortex shedding or l conditions that are drag dominated, to the detriment of the VAWT cycleeaveraged CP. Within realistic ﬂuctuation frequencies, faster ﬂuctuations marginally improve the performance of the VAWT. Shahzad et al. [12] numerically analyzed the performance output of a VAWT that features 12 equally spaced rotor and stator blades, respectively. The performance of the VAWT was monitored under an accelerated and decelerated gust of the value 1.09 m/s2 characterized by change in velocity from 4 m/s to 10 m/s. Results showed that the instantaneous torque output varies signiﬁcantly when a gust of air is applied to the turbine. The torque outputs vary during accelerating and decelerating ﬂows, highlighting the effect of transient phenomena. The abrupt change in the instantaneous torque output of the turbine may give rise to highly transient loads on the turbine's structure which may induce heavy stresses on the turbine leading to structural failure. Kozak [4] developed an iterative procedure to optimize the VAWT's geometry using blade pitch in unsteady wind conditions. Results of his study showed that power output could be raised at lower tip-speed ratios by mitigating the adverse effects of dynamic stall using blade pitch. 2. Methodology 2.1. Numerical model of VAWT The 2D computational domain was divided into two distinct sub-grids (as shown in Fig. 1)da stationary sub-grid that is the rectangular outer zone, determining the overall calculation domain, with a circular opening centered on the turbine's rotational axis and a rotor sub-grid that is a circular inner zone, which shall rotate with rotor angular velocity. The 2D VAWT model was designed without the blade-support arm and blade ends, hence neglecting their effect on rotor power extraction. Two VAWT conﬁgurations were considered in this study: one with NACA 0025 airfoils (symmetric) and the other with NACA 1425 (with positive blade camber) airfoils. Rotor diameter was set to 3 m. The VAWT has three blades, each with a chord length of 0.15 m. All geometry and mesh of the model were generated using Ansys ICEM CFD. Each blade of the rotor was meshed with a total of 210 nodes, with clustering both in the leading and trailing edges where high gradients in pressure and ﬂow were expected (Fig. 2a).

Fig. 1. 2D computational model.

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The mesh was generated from an O-type block formed around the airfoil (Fig. 2b). The ﬁrst cell height was set ensuring a yþ not exceeding 5. The yþ values of the full last rotation have been extracted and presented in Fig. 3. The maximum yþ values reached to about 2.7 and average values for all three airfoils range from 0.63 to 0.69. The cells expand from the wall to the O-type block boundaries with a growth rate of 1.1, giving a minimum of 90 layers within the said block. Cells beyond this block were set to have a maximum cell height not to exceed 0.10c for the rotor sub-grid. A smoothing algorithm was then applied to reduce the angle skewness of the cells. The created rotor mesh has a total of 176,898 cells with maximum orthogonality of 0.42, maximum aspect ratio of 617.2 and mean skewness of 0.10. The outer farﬁeld mesh, on the other hand, has a total of 74,575 cells with maximum orthogonality of 0.63, maximum aspect ratio of 6.96 and mean skewness of 0.16. All in-all, the computational domain has a total cell number of 251,473 with an overall maximum orthogonality of 0.42, maximum aspect ratio of 617.2 and mean skewness of 0.16. One critical factor that dictates the overall quality of the computational domain is the spatial resolution of the mesh near the blade [13]. To optimize the model, parametric study of node density was carried out prior to actual unsteady wind simulations. The appropriate surface node density was determined by doing initial steady wind simulations wherein three surface node densities (70, 210 and 300 airfoil nodes) were tested at l ¼ 4. The blade torque coefﬁcients in one full rotation for each case were compared. Results showed that while the torque curve of the mesh with 70 airfoil nodes greatly deviates from the curves of the other two cases, there is a very close agreement observed between the curves

Fig. 2. The present CFD model mesh: (a) near blade mesh, (b) O-type mesh within the rotating domain.

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Fig. 3. yþ values for the last rotation at l ¼ 4.

of the 210 and 300 airfoil nodes, such that they overlapped in most areas. The DCP computed between these two cases was only 0.0025 or 0.825% difference in magnitude. Given this very minimal variance, the grid with 210 airfoil nodes was chosen since it can give accurate results as that with 300 nodes but at a lesser computational time. To ensure proper unsteady simulation of the VAWT, sufﬁcient temporal resolution is required. Two different time step sizes, Dt equivalent to speciﬁc rotational displacements along the azimuth (Dt ¼ 1 u1 and Dt ¼ 0.5 u1) were tested at l ¼ 4. Though results from both test cases are comparable with very minimal DCP of 0.0036 or 1.17% difference in magnitude, the adapted time step size for the all succeeding simulations is still the lower Dt ¼ 0.5 ue1 for more accurate results. Lower residuals of the conserved variables were observed in the iterative computations using said time step, with maximum values reaching only up to 1 104 versus the observed residuals using Dt ¼ 1 u1 that reached as high as 1 103. The solution was considered converged if the residual results for all conserved variables fall below or equal to the set convergence criteria of 1 104. The outer stationary sub-grid on the other hand, was meshed relatively coarser than the rotor sub-grid to reduce computational time. Minimum cell height was set to one chord length. Cell growth height from the circular interface to the wall boundaries was to 1.1 giving a maximum cell height of 0.25 m. To avoid solid blockage and to allow full development of the wake, boundaries were positioned far enough from the rotor test section. The side boundaries and inlet distances were set to 5 diameters away from the rotor while outlet distance was set to 10 diameters away as suggested for testing VAWT in open ﬁeld scale [13,14]. The current symmetric and camber-bladed CFD models were validated with results of the QR5 wind tunnel test as cited by Scheurich [15] and the DMS model by Wahl [16]. As seen in Fig. 4, the current model compares well with the two other models in terms of the general trend of CP curve with optimum CP occurring at l ¼ 3.5e4. Close results are observed between the current and Wahl's models, with minimal variation which can be attributed to the difference in numerical model used e DMS vs. CFD. On the other hand, though very similar trend was also observed from the

results of the wind tunnel experiment of QR5, its relatively high CP magnitudes may be due to its optimized blade conﬁguration, which is helically twisted. Initial results also showed better performance of camber-bladed VAWT compared to its symmetric counterpart.

2.2. Unsteady wind simulation The computational domains generated were imported into the CFD code FLUENT v14.5 for numerical iterative solution using sliding mesh technique. The rotational motion was simulated by allowing the rotor sub-grid to rotate at constant angular velocity. The mesh movement was deﬁned explicitly by specifying timevarying positions for all the rotor sub-grid block cell vertices. An interface boundary surrounding the rotating sub-grid within the model was allowed to slide at speciﬁed velocity to represent its relative motion to the stationary sub-grid. The coupled pressureebased solver was selected with a second order implicit transient formulation for improved accuracy. All solution variables were solved using second order upwind discretization scheme since most of the ﬂow can be assumed to be not in line with the mesh. Unsteady wind simulations were carried out by specifying the magnitude of the velocity inlet as a time-dependent variable. Speciﬁcally, the inlet boundary condition was set to a mean wind speed of Umean ¼ 5 m/s with ﬂuctuating amplitude of Uamp ¼ ±10% (±0.5 m/s). Simulations were initially carried out at ﬂuctuation frequencies fc ¼ 0.5 Hz and fc ¼ 1 Hz but was later determined that varying the unsteady wind fc induced insigniﬁcant effect to VAWT performance, hence discussions were limited on comparing the results from one fc case (fc ¼ 1 Hz). The rotor angular speed is a constant u ¼ 13.33 rad/s that is the angular speed at l ¼ 4 where the optimum CP of VAWT in the steady wind case was achieved. The total number of VAWT rotations under gust to complete one full wind cycle can be computed by the following notations as suggested by McIntosh et al. [17].

nrev ¼

lmean pkgust

(1)

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Fig. 4. CP curves vs. l of various NACA XX25-bladed VAWTs.

where nrev is the number of rotor rotations in one wind cycle, lmean is the mean tip speed ratio computed from the varying values of u as a response to unsteady U∞ given by lmean ¼ umeanR/Umean and kgust is the reduced gust frequency equal to 2R/Dg. Dg is the variation in wind speed experienced by the VAWT during a gust and is equal to Umean/fc. Hence, kgust formula can be rewritten to kgust ¼ 2Rfc/Umean. For VAWT simulations with inlet boundary conditions set at Umean ¼ 5 m/s, ﬂuctuating amplitude Uamp ¼ ±10% (±0.5 m/s) and ﬂuctuation frequency fc ¼ 1 Hz, the gust length Dg is 5 m. The mean tip speed ratio is l z 4.02, hence completing one wind cycle with about 2.13 rotations at a constant VAWT rotational speed of u ¼ 13.33 rad/s. To ensure that a fully converged set of adjacent solutions is attained, a total of 21 full rotor rotations were simulated for each unsteady wind case. That is, for a half degree rotational displacement along the azimuth, about 15,120 time steps. 50 maximum iterations per time step was set for numerical computation. Solution is considered converged when residuals of all conserved variables is less than or equal to 1 104. 3. Results and discussion 3.1. Variation of Tb, l and a with unsteady U∞ The blade torque (Tb) curves of all three blades over 21 rotations, together with the ﬂuctuating wind stream, are shown in Fig. 5. As illustrated in the ﬁgures, the ﬁrst three rotations of the VAWT showed unconverged set of Tb as reﬂected by the erratic trend of torque curves within the said range. The results were similar to that of the steady wind case where full convergence per time step was achieved only after several rotor rotations when residuals of all conserved variables were observed to fall below 1 104. To complete 21 rotor rotations, a total of about 564 processor hours was required for each run of unsteady wind simulation using an Intel-based computer with 4 cores of Intel® Core™ i7-3770 3.40 GHz processors. The torque produced at each blade for all test cases are observed to be mostly positive in magnitude. This indicates a positive overall performance of the VAWTs. To illustrate and explain the VAWT performance under unsteady wind, the focus of the succeeding discussions are the fully

converged data generated from the last complete gust period. As seen in Fig. 6, approximately two rotor rotations are needed to complete one wind cycle with ﬂuctuation frequency fc ¼ 1 Hz, which supports the results from equation (1). Hence, rotor cycles 17th to 19th were considered. At constant u, an inverse relationship is observed between l and the ﬂuctuating U∞. An increase in U∞ induces a corresponding decrease in l. Having a Umean ¼ 5 m/s and a ﬂuctuating amplitude set to 10%, the maximum U∞ reaches up to 5.5 m/s and a minimum of 4.5 m/s. The maximum U∞ was recorded at the middle of the ﬁrst rotor cycle with a corresponding minimum l ¼ 3.64. The maximum a within the range of increasing U∞ were recorded at ±15.68 . Depending on the blade on subject, the values occur within the ﬁrst rotor cycle at 1 Hz unsteady wind. The minimum U∞, on the other hand, occurs at the middle of the second rotor cycle with a corresponding maximum l ¼ 4.44. For this range, extreme values of a were recorded at ±13.20 depending which blade is considered. The variation of the total combined torques TB of VAWTs, with the ﬂuctuating wind velocity U∞ at Uamp ¼ 10% and at fc ¼ 1 Hz is shown in Fig. 7. As illustrated, similar to the individual torque Tb of each blade of the VAWT, the total combined torque TB follows a positive trend with the increasing wind velocity. The maximum combined torques were computed to be 13.99 Nm and 14.78 for the symmetric and 1.5%-cambered blade, respectively, both occurring within the ﬁrst rotor cycle where the maximum U∞ was also recorded.

3.2. Variation of power and CP with unsteady U∞ Wind power PW and rotor power PB data, together with the resultant CP for one wind cycle are illustrated in Fig. 7. Rotor power depends primarily on the magnitude of torque produced by the blades, hence was expected to show the same trend as that of the total torque curve with respect to the intensity of wind. PB also increases with the increasing wind velocity U∞ and wind power PW, just like the total combined torque curve does. At fc ¼ 1 Hz, the maximum PB was computed at 186.33 Watts for the symmetrically bladed VAWT and 198.99 Watts for the camber-bladed VAWT occurring at the point of rotation where the PW was recorded high with a value of around 304 Watts. Unsteady wind results show conformity with the steady wind results in terms of which VAWT

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Fig. 5. Unsteady Tb and U∞ curves over 21 VAWT rotations.

conﬁguration performed better in relation to the magnitude of the power output. The power generated by the 1.5% camber-bladed VAWT was predicted to be comparatively higher than that of the symmetric-bladed VAWT, marking a 6.36% difference between these two PB values. The instantaneous unsteady CP curves of the symmetric and camber-bladed VAWT for said case were also illustrated in Fig. 8. These curves were consequently ﬁtted with their corresponding quasi-steady CP trend lines. It is apparent from the graph that the camber-bladed VAWT performs better with its instantaneous CP curve on top of that of the symmetric-bladed VAWT, all throughout

Fig. 6. Variation of l and a with U∞.

Fig. 7. Variation of total rotor torque with U∞.

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Fig. 8. Variation of power and CP through one wind cycle.

one wind cycle. A constant CP difference of about 0.03e0.05 can also be observed between the quasi-steady curves of the two VAWT proﬁles. There is an 11% difference in instantaneous CP magnitude between the two cases, in favor of the VAWT with camber blades. The cycle-averaged wind power was computed to be equal to 233.13 Watts. This value, together with the computed average PB, was subsequently used to compute for the cycle-averaged power coefﬁcients. The cycle-averaged PB, PW and CP of all test cases from the unsteady wind simulations, together with the steady wind results, were computed and tabulated in Table 1. Similar to steady wind data, the VAWT with cambered airfoils generated higher power in unsteady wind e 74.96 Watts versus 66.92 Watts of the symmetrically bladed VAWT. This is also reﬂected in the computed cycle-averaged CP (0.31 at lmean ¼ 4.02) for the camber-bladed VAWT, that is higher compared to the computed cycle-averaged CP of 0.28 (lmean ¼ 4.02) for the symmetrically bladed VAWT. On the other hand, by comparing these unsteady results to the steady wind data, it can be generalized that unsteady wind could have a detrimental effect to the performance of VAWT. As can be seen

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from the table, the cycle-averaged unsteady CP of the camberbladed VAWT is lower than the maximum CP of the same VAWT proﬁle in steady wind. A 9% drop in CP from 0.34 (l ¼ 4) to 0.31 (l ¼ 4.02) was recorded. The reason behind this drop in CP can be attributed to the poorer performance of the rotor in unsteady wind despite a higher value of recorded cycle-averaged wind power. Cycle-averaged unsteady rotor powers were computed to be equal to 66.92 Watts (symmetric) and 74.96 Watts (camber) at a cycleaveraged wind power of 233.13 Watts, versus the averaged steady rotor powers of 70.63 Watts (symmetric) and 78.32 Watts (camber) at a constant 229.69 Watts wind power. Putting the instantaneous unsteady CP data into a graph (see Fig. 9) overlaid with the steady CP, the extreme variations of VAWT performance under unsteady wind became apparent as unsteady CP exceeded the limits of that of the steady CP. This showed similar results to the study conducted by Danao [13] and Scheurich and Brown [5] on VAWT performance under unsteady wind condition. Their ﬁndings showed that unsteady CP ﬂuctuates within the range of the steady CP where the interval plot of steady CP was placed overlapping with the unsteady CP curve. The values vary with a maximum CP of the symmetric and camber-bladed VAWT recorded at 0.61 (lmean ¼ 3.64) and 0.65 (lmean ¼ 3.64), respectively. These maximum values of CP occur approximately in the middle of the ﬁrst rotation as shown in Fig. 8. The minimum CP on the other hand were 0.01 (symmetric) and 0 (camber), which were both recorded at lmean ¼ 4.4, occurring in the middle of the second rotor cycle. The quasi-steady CP was represented by the ﬁtted moving average trend line. Increasing the velocity of the wind causes the l to decrease as previously shown in Fig. 6 while inducing an increase in the quasi-steady CP. Decreasing wind velocities, on the other hand, cause the CP to drop below the steady CP curve as the l rises. Comparing the two quasi-steady curves, it can be observed that the maximum and minimum CP values were both higher for the camber-bladed VAWT than the symmetrically bladed VAWT. The maximum CP of the former is somewhat beyond 0.40. The latter's maximum CP, on the other hand, is lower at below 0.40. Similarly, minimum CP of the former is higher at a value beyond 0.20 versus the latter's minimum CP at approximately 0.2. In general, the quasi-steady curve does not follow the steady performance curve of the VAWTs at U∞ ¼ 5 m/s, for both the symmetric and camber-bladed unsteady CP. Results show that the quasi-steady CP curves vary with the ﬂuctuating wind, cutting across the steady CP curve. These ﬁndings are found to be very similar to the observations of Danao [13] in his study on the unsteady performance of a wind tunnel scale VAWT. His results showed that unsteady wind simulations have a fundamental relationship between VAWT CP and Reynolds number and that CFD data show a CP variation in unsteady wind that cuts across steady CP curves. Results from other related studies, however, such as works by McIntosh et al. [17] and Scheurich and Brown [5] on a similar VAWT scale (5 kW scale), are not consistent with the observed unsteady VAWT performance from the current study. They theorize that unsteady wind performance closely follows the steady CP curve when the unsteady mean l is higher than the optimum l for steady wind. Though Scheurich and Brown observed

Table 1 Comparison between steady and unsteady VAWT performance. Wind conditions

Test cases

Mean rotor power, N

Mean wind power, N

Mean CP

lmean

Steady Wind

Symmetric Camber Symmetric Camber

70.63 78.32 66.92 74.96

229.69 229.69 233.13 233.13

0.31 0.34 0.28 0.31

4.00 4.00 4.02 4.02

Unsteady Wind

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0.79 was predicted for cycle 1 and 0.39 for cycle 2. The maximum drag coefﬁcient in the upwind and downwind of the ﬁrst cycle loop were both high at Cd ¼ 0.14 and Cd ¼ 0.09, respectively. Lower peaks were observed for the cycle 2 loop, which were Cd ¼ 0.08 (upwind) and Cd ¼ 0.05 (downwind). For the cambered blade (Fig. 11), maximum Cl was recorded at 1.01 in the upwind and 0.88 in the downwind, both occurring within the ﬁrst half of the wind cycle (Cycle 1) where wind speeds were also observed high. Comparing these values to that of the symmetric blade results for the same gust period location, a slightly higher Cl in the upwind was recorded for the symmetric blade. But in the downwind, a signiﬁcant increase in lift generation was observed for the cambered blade. For the second half of the gust period (Cycle 2), maximum values of Cl were lower at 0.66 (upwind) and 0.44 (downwind), compared to cycle 1 values. Cambered blade generates higher lift in the downwind side compared to the symmetric blade, just like in cycle 1. The maximum drag coefﬁcients were also observed during the ﬁrst half of the wind cycle with values of 0.13 (upwind) and 0.11 (downwind). For the second half of the wind cycle, peak values of drag coefﬁcient were computed to be 0.08 in the upwind side and 0.05 in the downwind side. 3.4. Flow visualizations Fig. 9. Variation of the steady and unsteady CP.

similar results in terms of the large ﬂuctuations of unsteady CP even at low Uamp of 10% (within the limits of the steady performance), their claim is that VAWT with swept blades essentially traces the steady CP performance curve when subjected to unsteady wind with low fc. Similarly, McIntosh et al. concluded that at low fc ¼ 0.05 Hz, the quasi-steady CP traces the steady CP curve at l higher than unsteady mean l. 3.3. Lift and drag coefﬁcients over one wind cycle The lift and drag coefﬁcient loops of the VAWTs are shown in Fig. 10 and Fig. 11. For the symmetric-bladed VAWT (Fig. 10), the maximum lift in the upwind (0 < a < 15.68 ), with a magnitude of 1.03, occurs at the ﬁrst rotor cycle where the highest intensity of wind speed was also recorded. On the other hand, the peak value of the lift coefﬁcient for the 2nd cycle is lower at Cl ¼ 0.70, where wind velocities were rather low. In the downwind side, maximum Cl of

The variations of wind velocity, tip speed ratio and torque over one wind cycle are re-illustrated in Fig. 12. As can be seen from the unsteady wind proﬁle, high velocities were recorded during the ﬁrst rotor cycle (0 < q < 360 ) which correspond to increased torque generation and low l within the range. For ﬂow ﬁeld visualizations, the blade positions from this rotor cycle were considered since more ﬂow features can be expected and captured within this range. Conversely, higher l would merely show ﬂow ﬁeld that are mostly attached, to no ﬂow separation at all. The z-vorticity images of one blade of the VAWT proﬁles under investigation, at various azimuthal positions q, are shown and compared in Fig. 13. Stall on the blades become deeper as wind velocity increases from q ¼ 30 to q ¼ 150 , caused by the decreasing l. At q ¼ 30 , there is no visible ﬂow separation observed. Separation point starts to crawl on the suction side surface of the airfoil from the trailing edge to mid-chord when the blade is located at the azimuthal position q ¼ 90 and to point beyond mid-chord when blade is at q ¼ 150 . This behavior can be explained by looking at the torque proﬁle (Fig. 12b) wherein the magnitude of torque continues to increase from q ¼ 30 until it reaches a peak at approximately q ¼ 90 where a

Fig. 10. Lift and drag coefﬁcient loops of the symmetric blade over one wind cycle.

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Fig. 11. Lift and drag coefﬁcient loops of the cambered blade over one wind cycle.

is close to maximum generating a lot of lift at this point. After this point, a constant drop in torque magnitude can be observed before reaching minimum just before q ¼ 180 . Attached ﬂow is seen in the downwind side of rotation as torque variation within said range can be described as ﬂat with no sudden drop or increase in magnitude, except for a distinctive negative trough at q ¼ 270 . Similar to that of the steady wind results, wake is generated by the traversing unsteady wind through the center hub of the VAWT which interacts with the blades at q ¼ 270 . In the vorticity proﬁles, shed vortices are shown interacting with the blades at this point. This causes a distinctive sudden drop of blade torque at this point of rotation as shown in Fig. 12b. As discussed previously, lift generation in the downwind side of rotation was observed to be better for the VAWT with cambered blades than that of with symmetric blades. On the other hand, drag generation of the two blade proﬁles are very comparable with only very minimal differences. These results translated to a higher torque prediction for the camber-bladed VAWT which can be clearly seen from Fig. 12b. Torque produced by the cambered blade is constantly higher than the torque generated by the symmetric blade which started after mid-rotor rotation until q ¼ 360 . The same was observed on the second half of the wind cycle. These results then eventually translated into an increased power generation and higher CP for the cambered-bladed VAWT than the symmetric-bladed one.

4. Conclusion Results showed that VAWT power output and CP increases with increasing wind velocity at a constant u as observed from the quasi-steady curves ﬁtted to the instantaneous data of these variables. However, comparing results between the two wind conditions, unsteady wind imposed a detrimental effect to VAWT performance. The cycle-averaged unsteady CP was lower than the maximum CP computed from the steady wind case, for a speciﬁc VAWT proﬁle. A 9% drop in CP from 0.34 (l ¼ 4) to 0.31 (l ¼ 4.02) was recorded for the cambered-bladed VAWT, for instance. Despite the fact that a higher value of cycle-averaged wind power was recorded, the VAWTs performed poorer in unsteady wind. Cycleaveraged unsteady rotor powers were computed to be equal to 66.92 Watts (symmetric) and 74.96 Watts (camber) at a cycleaveraged wind power of 233.13 Watts, versus the averaged steady rotor powers of 70.63 Watts (symmetric) and 78.32 Watts (camber) at a constant 229.69 Watts wind power. The reason behind this is that though higher blade torques were generated during the ﬁrst half of the wind cycle due to the increased wind speeds at this range, this was counteracted by the lower torques generated at the second half of the wind cycle. But still, for the unsteady wind condition, better performance was achieved by the camber-bladed VAWT as compared to the symmetric-bladed VAWT. Lift generation, especially in the downwind side of rotation, was observed to

Fig. 12. (a) Wind velocity, tip speed ratio and (b) torque proﬁles at different azimuthal positions.

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prediction for the camber-bladed VAWT. These results then eventually translated into an increased power generation and higher CP for the cambered-bladed VAWT than the symmetric-bladed VAWT. Generally, the unsteady CP does not follow the steady performance curve of the VAWTs at U∞ ¼ 5 m/s, for both the symmetric and camber-bladed VAWTs. Results show that the unsteady CP curves greatly vary with the ﬂuctuating wind, with the ﬁtted quasisteady curve cutting across the steady CP curve. Based from the results, it can be generalized that incorporating a positive level of camber to the blade design of VAWT can improve its overall performance.

Acknowledgment This research study was funded and supported by the ERDT Program of the Department of Science and Technology through the University of the Philippines e College of Engineering.

References

Fig. 13. Z-vorticity proﬁles of one blade of the symmetric and camber-bladed VAWTs from the ﬁrst half of the unsteady wind cycle.

be better for the VAWT with cambered blades while drag generation of the two blade proﬁles are very comparable with only very minimal variations. These results translated to a higher torque

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