Unsteady Flow Simulation and Dynamic Stall Behaviour of Vertical Axis Wind Turbine Blades

Transcription

1 WIND ENGINEERING VOLUME 35, NO. 4, 2011 PP Unsteady Flow Simulation and Dynamic Stall Behaviour of Vertical Axis Wind Turbine Blades Ning Qin*, Robert Howell, Naveed Durrani, Kenichi Hamada and Tomos Smith Department of Mechanical Engineering, University of Sheffield, Sheffield, S1 3JD, UK ABSTRACT This paper presents a computational study of a rooftop size vertical axis wind turbine with straight blades (H-type turbine). The computational model solves for the two-dimensional and three-dimensional unsteady flow fields around the turbine based on the unsteady Reynolds averaged Navier-Stokes equations and a sliding mesh technique to connect the farfield fixed mesh to the near field rotating mesh around the rotor. Interesting flow features such as dynamic stall around the blades and the interaction of the blade wakes with the following blades are illuminated. Comparison of the 2D and 3D simulations highlight strong three dimensional effects, including the blade tip losses and the effects of the blade supporting shaft and arms. These effects significantly degrade the performance of the VAWT under investigation, pointing a way for improving VAW T designs. Keywords: Wind energy, vertical axis wind turbine, Darrieus wind turbine, wind turbine performance, dynamic stall, numerical simulation, sliding mesh NOMENCLATURE b Blade length (m) c Chord length (m) C D C L C M C P D F N F T L V R V W a θ λ VAWT Drag coefficient Lift coefficient Moment coefficient Wind turbine power coefficient, or percentage of power extracted from the wind by the turbine Drag force (N) Force normal to the blade path (N) Force tangential to the blade path (N) Lift force (N) Resultant velocity (m/s) Free stream wind velocity (m/s) Angle of attack (deg) Azimuth angle (deg) Tip speed ratio Vertical Axis Wind Turbine * Corresponding author, n.qin@sheffield.ac.uk

2 512 UNSTEADY FLOW SIMULATION AND DYNAMIC STALL BEHAVIOUR OF VERTICAL AXIS WIND TURBINE BLADES 1. INTRODUCTION With rising concerns regarding carbon emission and its impact on the environment, wind power generation has become the fastest growing industry for renewable energy production with more than 30 percent annual growth rate (Global Wind Energy Council, [1]). In addition to large wind farms, both off-shore and on-shore, there is also a strong interest in harvesting wind energy within the built environment in urban, suburban and remote areas. Although most currently popular wind turbine designs are of the horizontal axis type, straight bladed Vertical Axis Wind Turbines (H-VAWTs) holds several advantages over Horizontal Axis Wind Turbines (HAWTs). Primarily, VAWTs have no need for yawing towards the wind, which simplifies the system, are quieter in operation due to lower blade-tip speeds, and have lower manufacturing and maintenance costs. These are important advantages in the built environment. However, the majority of research on VAWT design was carried out during the late 1970s and early 1980s, notably at the USA Department of Energy Sandia National Laboratory (Sandia National Laboratory Staff, [2]) and in the UK by Reading University, and VAWT Ltd., who erected several prototypes including a 500kW version at Carmarthen Bay. During the 1970s through to 1980s, extensive research projects were carried out in the UK to investigate the potential of fixed pitch H-VAWT for large scale power generation. In these projects, the high torque exerted on the torque tube caused mechanism failure on several occasions and the projects ended before any solution to the problem could be formulated [3]. It is well known that VAWT exhibits very complex unsteady aerodynamics. A rapid changes in angle of attack and the resultant wind velocity (hence the local Reynolds number) are experienced as blades rotate, which more often than not leads to the dynamic stall phenomenon. Previous researches performed by McCroskey et al. [4, 5] for aerofoil flows and Fujisawa et al. [6] for Darrieus wind turbines revealed complex mechanisms of dynamic stall, in which two counter-rotating vortices being generated and transported in the wake. In addition, virtual camber effect due to blade rotation further complicates the blade aerodynamics, as shown by Kim et al. [7]. The understanding of the fundamental aspects of the complex aerodynamics of VAWTs is crucial for a successful design of either small or large VAWTs. The application of Computational Fluid Dynamics (CFD) techniques for VAWTs has emerged in the recent years. Several studies relating to the detailed flow field and aerodynamic prediction of VAWTs have been performed previously with various degree of success. In a research carried out by Brahimi et al. [8], a computational code was used to perform two dimensional incompressible unsteady flow simulation on a Darrieus-type VAWT, including predictions of the dynamic stall. The present study focuses on investigating dynamic stall characteristics and simulation of unsteady flow around the blades on a fixed pitch straight bladed H-VAWT using computational fluid dynamics. Due to the relative high aspect ratio of the VAWT blade, simulation and analysis of two dimensional modelling of H-VAWT blades give an efficient way to evaluate blade profile performance away from the blade tips. Various numerical parameters have been studied regarding the numerical accuracy of the simulation. The key phenomenon of blade dynamic stall have been investigated in details. To illustrate the three dimensional effects, a full three dimensional unsteady simulation of the H-VAWT was carried out and the effects of blade tips, the support shaft and arms were investigated. Traditionally NACA 4-degits series have been employed for Darrieus-type VAWTs. Previous research on Darrieus-type VAWTs has employed NACA0012 [9], which shifted later to thicker aerofoil NACA0015 [10, 11] and NACA0018 [12]. The present study focuses on the analysis of NACA0022 aerofoil profiled blades.

3 WIND ENGINEERING VOLUME 35, NO. 4, THE VAWT DESIGN AND COMPUTATIONAL SET-UP A. Previous Work Previous work [13] by the authors highlighted strong three dimensional effects, including the blade tip losses and the effect of the supporting shaft. This study included the two and three dimensional CFD simulation with the wind tunnel data of a small scale VAWT model as shown in Figure 1. Figure 1: Small Scale VAWT Installed in the Wind Tunnel Some of the performance coefficient results from this study are presented in the Figure 2 to appreciate the differences predicted in two and three dimensional CFD results and their comparison with the experimental data. The comparison is made for oncoming freestream air at velocities from 4.31 to 6.27 m/sec with different rotational speeds of the VAWT. Due to the computational cost restriction, not all the experimental data points were simulated. It is evident from Figure2 that a more than 40% difference is observed in two and three dimensional simulations owing to the blade tip vortices, strong three dimensionality in the flow and central shaft. (In the three dimensional model, the supporting arms were not simulated). B. The Model A fixed pitch straight blade H-VAWT was considered in the present study for a rooftop sized VAWT. The design is shown in Figure 3, where the diameter of the rotor D = 2.5 m; the rotor blade chord length c = 0.2 m; the blade length b = 2 m and, as a result, the blade aspect ratio AR = b/c = 10. There are three blades, each connected to the bearing disc on top of the torque shaft by a supporting arm. Assuming the power coefficient of the design varies from 0.2 to 0.4, the rated power of the system at a rated wind speed of 12 m/s should be around 1 kw to 2 kw. The dimensions of the supporting arms in the three dimensional model are tabulated in the following table. Supporting Arm (cylindrical) Supporting Arm diameter ~ 32% c or ~ 0.064m Supporting Arm length 1.0 m Diameter of top disk of the central shaft 0.5 m with attached supporting Arms Diameter of the central shaft 0.17m

4 514 UNSTEADY FLOW SIMULATION AND DYNAMIC STALL BEHAVIOUR OF VERTICAL AXIS WIND TURBINE BLADES Figure 2: [a-c] Comparison of Performance Coefficient at Different Operating Conditions [13]

5 WIND ENGINEERING VOLUME 35, NO. 4, Figure 3: CAD model of H-type VAWT C. The Computational Domain And Mesh The grid generation packages, GAMBIT and TGrid, were used to create the model geometry and the mesh. At the first stage of the investigation, two dimensional models were created in order to investigate the effects of aerofoil shape variations on the overall aerodynamic performance of the blades. These 2D models include the three rotating blades but not the supporting arms, the bearing disc or the supporting arms. Due to the high aspect ratio of the rotor blade, the relatively more computationally efficient 2D models serve the purposes of numerical parametric study and blade section aerofoil design. In order to maintain a high quality mesh around the blade during the blade revolution, a zonal approach in the mesh generation has been taken. The computational domain consists of two mesh zones, the inner rotor zone and the outer far-field one. The inner rotor zone contains three symmetric aerofoils placed on the circular rotation path with zero pitch, spaced equally at 120 apart from each other. The outer domain has a rectangular outer boundary representing the far-field with a circular hole to fit in the inner rotor zone. To examine the blade tip effects as well as the effects of the presence of the support arms, the torque shaft and the bearing disc, a three dimensional model was later generated. In this case, a cylindrical zone is created around the blade, which is embedded inside a far-field fixed cube mesh. Views of the 3D mesh can be found in Figure 4. The local structured meshes around the blades are refined for accurate and efficient resolution of the boundary layers and the wakes. The overall hybrid mesh gives the flexibility for dealing with the other components of the wind turbine. In order to predict the overall torque generated by the blades for the whole rotation with time accurate solution, a sliding mesh technique was applied to the rotating circular area for the 2D model and cylindrical tube volume for the 3D model. The contribution of the torque is considered only from the blades of the VAWT. This will enable us to compare the results with the 2D simulations due to flow interaction. The effects of the supporting arms, central shaft and the top disk (holding the supporting arms) are shown collectively by the difference in the results of the 2D and 3D simulations. The meshes within the circle (2D) or the tube (3D) rotate about the axis of the turbine while the outer domain was set stationary, with the interface of the two zones sliding against each other. The 2D solution domain size is 10 m by 6 m (in other words, 50c by 30c, where c is chord length), which is chosen based on our previous numerical studies [15] on the effects of the numerical far field boundaries. These numerical studies [15] were focused on testing

6 516 U NSTEADY F LOW S IMULATION AND D YNAMIC S TALL B EHAVIOUR OF V ERTICAL A XIS W IND T URBINE B LADES domains with different dimensions for the same case and evaluating the effect in results. A velocity inlet boundary condition too close to the rotor region will give incorrect results but after a certain distance, the results show little difference. Therefore, different simulations were done to select an optimized dimension of the domain. For 3D simulations, the same 10 m by 6 m domain as used in 2D simulations was used in the rotational plane and the z-dimension was taken as 4 m. Figure 4: 3D Domain: Boundary Conditions and Mesh (a) Whole Domain (b) Turbine Rotor (c) Disc, Arms and Shaft (d) Blade Tip For both 2D and 3D models, the free stream wind was modelled to enter from the left in the presentation of the results in this paper. Hence the left side boundary of the domain is defined as velocity inlet, where the inlet flow (wind speed) and turbulent quantities are specified. A turbulent intensity of 10% and a turbulent length scale of 0.01 m were applied at the inlet. This is based on the conventional assumptions and the incoming wind turbulence level is not the subject of the current study, although it may be a direction for future investigation. The boundary on the right of the domain was specified as an outflow boundary condition. At the outflow boundary conditions, all flow properties except pressure are extrapolated from the flow field while an outflow pressure is fixed. A no-slip boundary condition is specified at the blade and the supporting structural surface. This implies that the relative velocity at the wall is zero. The side boundaries are defined as the slip boundary conditions. This boundary condition is an approximation to represent the wind turbine in free stream with infinite far field boundary. The further away this far field boundary is the more accurate representation the boundary condition. However on the other hand this also means an increased computational domain and more computational time. As mentioned earlier, a choice of 50c x 30c were found to be sufficient for the current cases. Top and bottom farfield conditions were applied for the 3D model. In terms of near-wall treatment, the standard wall function was applied. During the complete rotational cycle, the effective angle of attack of the turbine blade varies from -20 to 20. Both interface boundaries of the rotor domain and the outer domain were defined as interface boundary designed for sliding mesh application. These imply interpolation of solutions between the two domains. Although the free stream wind velocity at the inlet of the domain was kept constant, due to the rotational motion of the turbine, the relative velocity which blades experience varies. The rel-

7 WIND ENGINEERING VOLUME 35, NO. 4, ative wind speed varied from 0 m/s to 84 m/s for a free stream wind velocity of 12 m/s and a rotational speed ranging from 100 rpm to 550 rpm. Furthermore the Reynolds number based on the chord length (Re c ) varies up to about for the relative velocity range. Strictly speaking, both laminar and turbulent flows around the blades are expected within this range. However in the present study, the flow was assumed to be fully turbulent. It is believed that this assumption will not affect the general conclusions from the study, as the flow is predominantly turbulent. Another popular definition of Reynolds number for wind turbines is based on the rotor disc diameter and the wind speed, i.e. DU/n, which gives Re 2x10 6. Note that this is significantly higher than the Reynolds number of 3000 in Fujisawa et al. s water tunnel tests[6], which explains the difference in the vortex shedding behaviour between the two models discussed later in the paper. Unstructured meshes were applied to both the rotor away from the near surface region and the outer grids. Finer meshes were used around the blades and regions in the wake of the blades. Particularly, regions at the leading edge, trailing edge and in the middle of blade were finely meshed in order to capture the flow field more accurately. The outer mesh was coarsened in regions expanding away from the rotor in order to minimise the CPU time. Grid sensitivity study was carried out before the final dimension of the mesh was chosen. The quality of the mesh was also checked against mesh quality criteria as well as the y + values around the blades, which is important for the turbulence modelling. The wall y + for 3D model remained between 3 and 100, which is the range for the standard wall function to be valid. Due to computational time limitation, the 3D mesh has to be coarser in compared with the 2D mesh if a plane section in Z (spanwise) is taken. Also, due to the rotor shaft and support arms, the grid density is not uniform and is different at spanwise locations. Hence, it is difficult to carry out a direct comparison between the grids for 2D and 3D simulations. The total number of cells for the 3D model was about 2 million. The computational cost and time for this mesh size is very extensive considering full 3D unsteady calculations with the available resources. After balancing the mesh resolution and the computational affordability for the current simulation problem, it is believed that the important flow features are captured with the current mesh for the 3D model. However, it is noted that the computational domain can have a strong effect on the power coefficient as illustrated by Alidadi and Calisal [16], who showed that limited domains have an effect of increasing the power coefficient. D. The Flow Solver and the Turbulence Model In order to reflect the flow condition of VAWT, the constant density coupled solver in commercial software Fluent (version ) was employed. The method solves the governing equations of continuity and momentum simultaneously (coupled together) as a set of equations. Validation of the methodology has been conducted in a previous paper [13] by the authors through a parallel experimental and CFD study for a small scale wind tunnel VAWT model. The study indicated that 3D effects and wind tunnel wall effects are crucial in the simulations and reasonable comparison can be achieved if the wind tunnel test conditions are closely matched. The choice of the turbulence models influences the resultant flow field, the level of solution accuracy, and the required computational resource and time. The one-equation eddy viscosity models such as the Spalart-Allmaras model are often considered inappropriate when flow changes rapidly from wall bounded to a free shear flow. The two-equation turbulence models such as the standard k-ε, RNG k-ε, or realisable k-ε model may also be used. For HAWTs it was found that the standard k-ε model gave inaccurate results after flow separation in the previous research carried out by Wolfe and Ochs [14]. It is further noted that no turbulence model is strictly appropriate for separated flows and the RNG model is a better option than k-ε as it does not

8 518 UNSTEADY FLOW SIMULATION AND DYNAMIC STALL BEHAVIOUR OF VERTICAL AXIS WIND TURBINE BLADES use the fixed empirical coefficients based on well behaved turbulence experiments. For the present project, three types of k-ε two-equation turbulence models were examined. Standard k-ε, RNG k-ε and Realisable k-ε turbulence models were employed in the following comparison. The turbulent intensity is kept as default value of 10%. Both RNG and Realisable k-ε models resulted in higher torque generation than the standard k-ε model, as shown in Figure 7. When the vorticity magnitude contours of the standard and the RNG k-ε models were compared, it was found that the RNG k-ε models predicted relatively more compact but stronger vortices downstream of the trailing edge of the blade. Moreover the standard k-ε model predicted greater turbulence intensity. This stronger turbulent flow field resulted in smaller torque generated by the blade rotating through the domain. Furthermore the more intensive turbulent flow field resulted in more oscillatory torque in the downwind (after azimuth angle of 180 ). It is known that both RNG and Realizable k-ε models predict flow field more consistently than the standard k-ε model when the flow features include strong streamline curvature, vortices, and rotation. However the realisable model has a limitation that it could sometimes produce nonphysical turbulent viscosities when the computational domain contains both rotating and stationary fluid zones, which is the case in the present research. Therefore the RNG k-ε model was chosen for the present simulations in the following work. Nevertheless, this argument cannot replace the necessity of experimental validation of the physical model for such a complicated flow including dynamic stall. E. Grid Sensitivity Study These tests are carried out for the 2D model. Different numbers of cells on the base-line case (NACA0022 aerofoil, wind speed V w = 12m/s, tip speed ratio λ = 3) were simulated in order to perform grid sensitivity study. Figure 5 shows the sensitivity of the blade torque of one of the blades to the mesh resolution. While there is a large difference from the coarse to the medium mesh, it was observed that there was very little difference in the solution between the medium and the fine meshes. Therefore the solution with the medium mesh gives sufficient spatial mesh resolution. The azimuth angle is defined as zero as the blade is at the position moving towards the wind from the leeward side to the windward side. As can be seen from the figure, a much larger amount of energy is extracted from the windward side with the maximum at about 90. Due to the computational cost, no further systematic grid sensitivity study could be carried out for the 3D unsteady calculations. Figure 5: Grid Sensitivity Study: Torque vs. Azimuth Angle F. Temporal Discretisation and Time Step Due to the nature of the flow around the VAWT blade, unsteady flow simulations are required. For such flows, the temporal terms in the flow governing equations have to be included and dis-

9 WIND ENGINEERING VOLUME 35, NO. 4, cretised and a solution is obtained for each time step. Appropriate time stepping has to be found so that the CPU time for iterations would be minimised while obtaining a numerically accurate solution. Figure 6 shows the sensitivity of the solution against different time step sizes. No difference in the results was found when time step of seconds and seconds were compared whereas a time step of results in overestimating the torque in comparison with the smaller time steps. The time step of seconds was therefore chosen for the following solutions. Figure 6: Time Step Study: Torque vs. Azimuth Angle Figure 7: Comparison of Different Turbulence Models: Torque vs. Azimuth Angle G. Achieving Convergence The convergence criterion for all the parameters was set to 10-4 at each time step. At the start of simulation, the periodic flow field took some time to be established, as shown in Figure 8. Several revolutions had to be simulated before converged periodical solution was obtained. Figure 8 shows the initial torque generated, which is less than the stabilised periodical result for later cycles, apart from a narrow peak (short duration before settling down). The lower torque at the initial transient stage is due to the lack of lift generation of the blade rather than the formation of the wake, as the wakes do not disappear at the later stage. At the initial stage the unsteady flow around the blade is not established to generate decent lift, and therefore the torque, in the windward side. Furthermore for some cases, first order upwind discretisation was used during the starting-up process then once the solution became nearer to the periodic solution, second order upwind discretisation was employed.

10 520 UNSTEADY FLOW SIMULATION AND DYNAMIC STALL BEHAVIOUR OF VERTICAL AXIS WIND TURBINE BLADES Figure 8: Periodical Torque Results over 6 Cycles 3. RESULTS The power coefficients (Cp) variation over a range of TSR values for different aerofoils was studied previously by the authors [15] for the selection of the best suited airfoil and its optimum performance coefficient with respect to TSR. It was concluded that although at higher TSR values (typically 3.5 and 4.0) the 12% and 15% thick NACA symmetrical airfoils give better performance for different oncoming wind speeds; the best overall performance is achieved by 22% thick symmetric NACA airfoil. This lead to the selection of 22% chord thickness aerofoil NACA0022 with optimum conditions at 12 m/s with tip speed ratio TSR = 3. All studies in 2D and 3D in this paper are done at these conditions. A. Two Dimensional Unsteady Flow Field The unsteady flow field is expected to be complex particularly due to the wake effects. It can be observed from both velocity and vorticity magnitude plots in Figure 9 that the wake from the leading blade interacts with the following blades. Hence the efficiency of the downstream blades is affected due to impinging wakes. Figure 9: Contour of Velocity Magnitude (Left) and Vorticity Magnitude (Right)

11 WIND ENGINEERING VOLUME 35, NO. 4, For blade 1, at an azimuth angle θ = 0 (α = 0, upward direction due north in Figure 10), a negative torque is generated and the minimum torque is reached at approximately θ = 13 (α = -3 ). Around this position, the torque is drag dominated and the lift makes very small contribution to the positive torque as it acts close to the normal direction of the rotation. After θ = 13, the torque starts to increase due to the lift direction change, which becomes more favourable for positive torque contribution. In the meantime, more lift is created as the magnitude of the relative angle of attack increased. Positive torque reaches its maximum at about θ = 90 (windward direction, due west in Figure 10). After the peak, the drag begins to increase as the blade enters into dynamic stall, and as a result, the torque decreases. Near θ = 180 (due south), the torque becomes negative as the drag starts to be dominant. In the leeward path, 180 < θ < 360, a smaller positive torque is generated. Since the wind power is a function of V 3 w, a small reduction in the wind speed upwind gives a rise to a large reduction in possible power extraction. The mechanism of a blade rotating through the wake of the previous blade also reduces effective power extraction. This phenomenon can be seen in Figure 10. By combining torques generated by the three blades, the total torque ripple can be produced as shown in Figure 10. Figure 10: Total Torque Ripple B. Discussion on Dynamic Stall Behaviour of VAWT Blades For a pitching aerofoil, the dynamic stall phenomenon can be illustrated by plotting the instantaneous lift against the incidence. The presentation of such analysis of dynamic stall for the flow around the VAWT blade aerofoil is more complicated because the relative velocity vector to the blade aerofoil changes in both direction and magnitude. To study the instantaneous lift coefficient against incidence, the instantaneous velocity magnitude should be used in the lift and drag coefficient definition. On the other hand, to investigate the comparative behaviour around the azimuth, a single velocity magnitude is required for the definition. The 2D schematics of the VAWT are described in Figure 11. In order to quantify dynamic stall characteristics of the VAWT rotor blades, two types of C l,i were calculated in the present analysis using the varying relative velocity V R and the mean relative velocity. The basic definition of the resultant velocity and the angle of attack are as follows:

12 522 UNSTEADY FLOW SIMULATION AND DYNAMIC STALL BEHAVIOUR OF VERTICAL AXIS WIND TURBINE BLADES (1.1) (1.2) Figure 11: Schematic of 2D VAWT with explanation of different terminologies Graphs of these two types of lift coefficients against angle of attack for the NACA0022 baseline case are plotted in Figures 12(a) and (b). The force data in X and Y directions are extracted from the solution and converted into instantaneous lift force generated by the blade aerofoil. From Figure 12(a), at θ = 0 (α = 0 ), not surprisingly, almost no lift is generated. Instantaneous lift coefficient increases almost linearly in the negative direction up to θ =79.2 (α = ) and stall occurred with the maximum instantaneous lift coefficient of Note that the maximum static lift coefficient is and stalls at α = -15 from the static lift coefficient curve for this aerofoil from previous work [15]. It can be concluded that the blade aerofoil resulted in a higher lift coefficient with a delayed stall angle of 2. As the incidence increases further, it reaches its maximum incidence (a MIN = ) at θ = 110. In contrast to the θ = 0 case, a relatively high instantaneous lift coefficient could be seen at θ=180 even though the incidence α = 0 due the dynamic effects and the difference of the flowfield in and out the rotor path. Inside the rotor path, the wake generated by the windward blade travels into the leeward side and interacts with the blade downstream.

13 WIND ENGINEERING VOLUME 35, NO. 4, On the leeward side (on the right half of the rotation circle), the lift curve takes a lower slope, reaching a maximum at about α = 15. The stall is milder in comparison with the dynamic stall on the windward side and the maximum lift coefficient lower. (a) (b) Figure 12: (a) Instantaneous Lift Coefficient vs. AoA, showing hysteresis loop (b) Adjusted Lift Coefficient vs. Angle of Attack (AoA)

14 524 UNSTEADY FLOW SIMULATION AND DYNAMIC STALL BEHAVIOUR OF VERTICAL AXIS WIND TURBINE BLADES Figure 12(b) shows another plot of the instantaneous lift coefficient, which was calculated using the mean V R =36m/s, against the incidence. This allowed a comparison of instantaneous lift through one rotation. The plot is a significantly different shape when the mean velocity is used in the instantaneous lift coefficient definition. The maximum lift is reached at θ = 64, earlier than that for the relative lift coefficient, while on the leeward side, the maximum lift is at a much later stage passing θ = 270. It can be seen that downstream lift generation is much lower than that generated upstream. This implied the large differences in torque generation on the windward and leeward sides of the rotation. However, since the energy extracted (the torque) is related to the force in the tangential direction of the blade rotating path, the maximum torque is actually achieved, at θ = 90, in the region when the blade is beyond its stalling point. In other words, the maximum energy is extracted at the point when the blade is actually stalled. This is a very interesting and unique feature for VAWT blade aerodynamics, which is significantly different from the dynamic stall behaviour of the fixed wing of a manoeuvring aircraft or the rotor blade of a helicopter rotor. An implication of this behaviour may leads to designs of VAWT blades that incorporate dynamic stall conditions within the design envelope rather than avoid it at all cost. C. Results of Three Dimensional Model After the above systematic study of the various numerical and physical aspects of the VAWT blade aerofoil behaviours, a much more demanding 3D unsteady CFD analysis of the rooftop model was performed. The purpose is to reveal the three dimensional effects due to blade tip losses and the losses due to the supporting structures, which are neglected in the 2D study. This work has also been carried out to lay the foundations for comparison with wind tunnel test data and site tests for validation purposes. One such validation study was reported in a parallel paper by Howell et al. [13] at a smaller scale (lower Reynolds number) for a wind tunnel model including the wind tunnel wall effects. Figure 13 shows the torque created by one blade against the azimuth angle together with 2D model results under the same conditions. A number of significant differences can be observed. The 3D torque curve shape is similar to the 2D one but is shifted downwards, resulting in a significantly lower average torque by about 40%. This result shows a very strong effect of blade-tips and the additional loss from the support arms. A relatively more significant difference occurs in the leeward than in the windward path, where the positive torque is only produced between θ = 204 and 318 for the 3D model. Therefore a large portion of negative torque is generated through the leeward path. The blade-tip generates a trailing vortex, which interacts with the following blade. The obstructed flow due to the shaft and the flow interactions caused by support arms also contribute to the blade performance reduction in the leeward path. The influence of the support arms and the shaft influenced the flow filed is shown in Figure 14. Figure 14(a) shows the vorticity built up around the three supporting arms, representing losses due to the viscous effects (both profile and friction drags). Note that for the supporting arms, the drag acts directly against the torque generation as the velocity is always at a zero incidence to the profile section of the arms. Figure 14(b) shows the large blade-tip vortices generated at the blade-tips (see planes C and D in comparison with planes A and B), which travel into the leeward side of the rotor. Also significant in Figure 14(b) is the wake from the turbine s shaft, which further degrades blades performance on the leeward side. Note that the tested rooftop model has a relatively high aspect ratio of 10, indicating a strong 3D effect even for high aspect ratio blades.

15 W IND E NGINEERING VOLUME 35, N O. 4, 2011 Figure 13: Comparison of Torque Generation between 2D and 3D Models Figure 14: Vorticity magnitude Contours for the 3D Rooftop Model 525

16 526 UNSTEADY FLOW SIMULATION AND DYNAMIC STALL BEHAVIOUR OF VERTICAL AXIS WIND TURBINE BLADES The substantial three dimensional effects points a number of ways forward for improving the VAWT performance by alleviating these detrimental factors, for example, by relieving the blade tip losses, reducing drag of the supporting arms, and minimising the wake of the VAWT shaft. By doing so, the much higher power coefficient of the ideal 2D VAWT may be gradually approached. 4. CONCLUSION Numerical analyses of two dimensional unsteady flowfield on H-type VAWT blades have revealed significant influences of windward flowfield on the leeward blade performance. This explains a relatively lower wind power extraction potential when the blade is moving through the leeward azimuth angles. The dynamic stall study has shown a large difference in instantaneous lift coefficients in the windward and the leeward sides of the VAWT blades. Furthermore the dynamic stall behaviour for the VAWT blade has been found to be very different from that for a pitching aerofoil due to the variation of both the direction and the magnitude of the relative incoming velocity vector. An important finding is that the maximum torque during the revolution has been discovered at an azimuth angle beyond the blade stall. The three dimensional CFD model captured interesting phenomena, such as blade tip vortices and support arm profile and friction drags, in the VAWT operation. Strong three dimensional effects were observed in the flow fields regarding the tip vortices, the wake from the supporting shaft and arms, which result in a significant reduction in the wind power extraction rate. While these three dimensional interactions are complicated, the 3D blade torque exhibits a very similar curve as compared with the 2D results despite a significant shift downwards. It is therefore appropriate to conclude that the efficiency of the VAWTs may be improved substantially by minimising the three dimensional effects, in particular, the tip effects. REFERENCES 1. Global Wind Energy Council, 2005, Global wind power continues expansion pace of installation needs to accelerate to combat climate change [Accessed online 10/04/07: 2. Sandia National Laboratory Staff, Vertical axis wind turbines: the history of the DoE program, 3. Peace, S Wind alternatives: Why not vertical axis? Refocus Vol. 4 Issue 3, pp.30-33, McCroskey, W.J., Carr, L.W., McAlister, K.W. 1976, Dynamic Stall Experiments on Oscillating Airfoils. AIAA Journal, Vol.14, No.1, pp McCroskey, W.J. 1982, Unsteady Airfoils. Ann. Rev. Fluid Mechanics 14, pp Axis Wind Turbines. International Journal of Rotating Machinery, Vol.2, No.1, pp Fujisawa, N, Shibuya, S., 2001, Observations of Dynamic Stall on Darrieus Wind Turbine Blades. Journal of Wind Engineering and Industrial Aerodynamics, 89, , Kim, D.J., Yun C.Y., Park, I.H. Jung, J.S. 2003, Aerodynamic Loads Prediction of the Cycloidal Blades System of UAV Cyclocopter Considering Virtual Camber Effect. 14 th International Conference on Adaptive Structures and Technologies, Seoul, Korea. 8. M. T. Brahimi, A. Allet, and I. Paraschivoiu, Aerodynamic Analysis Models for Vertical-Axis Wind Turbines, International Journal of Rotating Machinery, vol. 2, no. 1, pp , doi: /s x Marini M., Massardo A., Satta A., 1992, Performance of Vertical Axis Wind Turbines with Different Shapes. Journal of Wind Engineering and Industrial Aerodynamics, 39, pp

17 WIND ENGINEERING VOLUME 35, NO. 4, Agren O., Berg M., Lejion M., 2005, A time-dependent potential flow theory for aerodynamics of vertical axis wind turbines. Journal of Applied Physics 97, Vandenberghe D., Dick E., 1987, A Free Vortex Simulation Method for the Straight Bladed Vertical Axis Wind Turbine. Journal of Wind Engineering and Industrial Aerodynamics, 26, pp Claessens M.C., 2006, The Design and Testing of Airfoils for Application in Small Vertical Axis Wind Turbines. MSc Thesis, Delft University of Technology, Faculty of Aerospace Engineering. 13. Howell R., Qin N., Edwards, J., Durrani N, Wind tunnel and numerical study of a small vertical axis wind turbine, Renewable Energy 35 (2010) Wolfe E.P., Ochs S.S., CFD Calculations of S809 Aerodynamic Characteristics. AIAA Aerospace Sciences Meeting, 35th AIAA Aerospace Science Meeting and Exhibit, Reno, NV, 1997, AIAA T.C. Smith, Aerodynamic design of wind turbine blades for maximum wind power extraction. MEng thesis, The University of Sheffield, Department of Mechanical Engineering, Alidadi, M.; Calisal, S., Effects of towing tank walls on the performance of a Vertical Axis Turbine, Oceans 2007, pp1-7.

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