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Quantification of the effects of geometric approximations on the performance of a vertical axis wind turbine
Renewable Energy 74 (2015) 661e670
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Quantification of the effects of geometric approximations on the performance of a vertical axis wind turbine M. Salman Siddiqui, Naveed Durrani 1, Imran Akhtar*, 2 Department of Mechanical Engineering, NUST College of Electrical & Mechanical Engineering, National University of Sciences & Technology, Islamabad 44000, Pakistan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 December 2013 Accepted 24 August 2014 Available online
With the soaring energy demands, an urge to explore the alternate and renewable energy resources has become the focal point of various active research fronts. The scientific community is revisiting the inkling to tap the wind resources in more rigorous and novel ways. Recent idea of net-zero buildings has prompted the realization of novel ideas such as employment of omni-directional vertical-axis wind turbine (VAWT) for roof-top application etc. Generally, owing to the high computational cost and time, different levels of geometric simplifications are considered in numerical studies. It becomes very important to quantify the effect of these approximations for realistic and logical conclusions. The detailed performance of a 2.5 m diameter VAWT is sequentially presented with various levels of approximations spanning from two-dimensional to complete three-dimensional geometry. The performance along with the flow physics with focus on tip effects, spanwise flow effects, effect of supporting arms and central hub is discussed. We conclude that two-dimensional approximation can over predict the performance by 32%. Similar trend is also observed for other geometric and flow approximations. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Vertical-axis wind turbine Geometric approximation Performance parameter Numerical simulation Sliding mesh
1. Introduction A substantial shift towards promoting the renewable energy is evident with the growing awareness of environmental pollution. Concerns about the global warming and depleting reserves of fossil fuels have further strengthened the drive to explore the alternative energy venues. Consequently, a revitalized interest in different related areas such as power generation through windmills is observed around the globe. One particular area in focus is about the suitability of using wind turbines to generate power in an urban environment. The idea to place a wind turbine on top of buildings may seem less than ideal as a first thought. This application has received considerable attention in net-zero building design. Nevertheless, the expected benefits in terms of clean and green power output have attracted a sizeable scientific community to explore this idea. Flow of air around a wind turbine housed over a building in a built up area requires consideration of different
* Corresponding author. E-mail address: [email protected] (I. Akhtar). 1 Visiting Faculty, Institute of Space Technology, Islamabad, Pakistan. 2 Also Adjunct Research Member, Interdisciplinary Center for Applied Mathematics, MC 0315, Virginia Tech, Blacksburg, VA 24061, USA. http://dx.doi.org/10.1016/j.renene.2014.08.068 0960-1481/© 2014 Elsevier Ltd. All rights reserved.
factors. These factors include variation in turbulence intensity and wind shear, change of direction of wind and distance of blades from the ground etc. Wind turbines are classified by their axis of rotation into two general types: horizontal axis wind turbine (HAWT) a vertical axis wind turbine (VAWT). Recently VAWT has received considerable attention due to inherent characteristics of omni-directionality, less noise, simplicity of manufacturing, mechanically able to withstand higher wind speeds and their efficiency when put on the urban rooftop building have revived the interest in VAWT. The flow physics is expected to be complex due to wake with flow structures of different length scales, high directional variability, large skew angles and increased turbulence intensity. To design an optimum configuration under various flow conditions, computational fluid dynamics (CFD) provides an affordable and a practical tool simulate the flow around the VAWT. Despite all the advancements in computer architecture and numerical methods, an exact computational fluid dynamic analysis, also termed as direct numerical simulation (DNS) is not possible. So, the simulations have to be limited by accepting approximations in conjunction with the desired level of accuracy and available computational time and cost resources. The challenges involve in the simulation include the rotational aspect of the rotor blades and ensuing vortex shedding, effect of central shaft and hub on the flow
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and wakeerotor interactions etc. Different geometric approximations are generally considered to do the numerical simulations of this highly complex rotating turbine cases. The flow governing equations are generally approximated using Reynolds-averaged Navier Stokes (RANS) for real time 3D flows due to their reasonable relative accuracy with less computational time. In literature, limited research work is available regarding the detailed aerodynamic analysis of VAWT using the CFD analysis. For detailed review of various configurations and design techniques of the VAWT, readers are referred to Ref. [1]. Hamada et al. [2], Durrani et al. [3,4] performed numerical analysis on a horizontal (H)-VAWT to study its aerodynamics. They analyzed the flow field and compared various blade profiles to determine the effect of blade thickness, blade fixing angle, thickness, camber effects and dynamic stall on the overall performance. Hwang [5] employed a commercial CFD package; (STAR-CD) for the performance predictions of the VAWT. He performed moving mesh analysis using the k-3 turbulence model. Ferreira et al. [6] investigated effects of different turbulence models, such as one equation SpalartAllmaras (S-A) model [7], on the flow field. Eriksson et al. [8] and Marini et al. [9] performed the aerodynamic analysis of the Darrieustype wind turbine. They also discussed different configurations of the VAWT and compared their effect on performance parameters. Brahimi et al. [10] developed a numerical algorithm known as “TKFLOW”. Results using TKFLOW could predict the region where the dynamic stall might occur. Claessens [11] performed the study to improve the performance of the NACA 0018 profile. He used the commercial tool RFOIL [12] and developed a numerical algorithm for the calculation of VAWT performance parameters. He proposed his own design of an airfoil and named it DU 06-W-200. He predicted that the proposed airfoil has increased structural strength, enhanced torque generation in the downwind path and results in smaller drop in lift coefficients as compared to the other airfoils. In this paper, we extend and build on the existing studies [13e15] on the performance of the VAWT. With recent advances in computing technology and available CFD software, it has become viable to conduct full scale simulations of the complete turbine. However, it is still not feasible to perform a complete set of simulations over a wide parametric range for multidisciplinary design optimization. Thus, researchers often resort various approximations on actual 3D VAWT. These approximations can be a simple 2D analysis, 3D analysis with top and bottom symmetry, i.e. infinite span with no tip effects, and 3D analysis with finite span including tip effects. In 3D analysis, some researchers exclude the support structure (support arms and central hub) to focus on VAWT blades only. Hence, it becomes very important to understand and quantify the effects of geometric approximation on turbine performance. Thus, the key objective of this work is to quantify the effects of different approximations employed in CFD analysis for a fixed VAWT design. In other words, we explore how good the 2D or 3D analysis to compute its performance parameters is. The quantification employs comparison of parameters torque ripple, overall torque, and the performance coefficient over a range of tip-speed ratio. 2. The computational model and setup 2.1. Geometric model The type of wind turbine in the present study is a fixed pitch straight blade Darrieus type H-VAWT as shown in Fig. 1. The turbine has a diameter of 2.5 m with 0.2 m chord length and blade length (span) of 2.5 m. Thus, the aspect ratio is 12.5 with no taper. We select NACA 0022 airfoil based on the previous work [14]. The baseline inlet velocity is 12 m/s for all the cases. The rated power output is expected to be around 2 KW.
Fig. 1. CAD model of 3-bladed H-VAWT with support arm and struts.
In order to numerically simulate the flow past the turbine, we generate the mesh using Gambit and then export it into the ANSYSFLUENT solver. Various geometric configurations to approximate VAWT design are tabulated in Table 1. We consider five cases ranging from a two-dimensional airfoil to a complete turbine model. Details of the grid points and simulation time per iteration are also provided. In the last column, a schematic of each case is shown to elaborate geometric approximation of the turbine model. Brief description of each case is also provided for better apprehension of the reader. For Case I, a 2D model of the turbine, comprising three airfoils (blades) 120 apart, is created. The support arms, central shaft and the disc are not incorporated in Case I. The domain size is set as 50c 30c (where c is the chord length), motivated by the fact that this domain size does not affect on the flow behavior of the rotating turbine [16]. The rotor computational domain is located at the center of the domain space. In order to enhance the quality of mesh generation, we employ a zonal approach. We create two computational domains; the rotor domain and the outer domain which are then connected together through “interfaces”. Tri-diagonal mesh concept is employed and the boundary layer and size function are used to generate a clustered mesh near airfoils. It helps in capturing the flow physics adequately. The yþ values kept under 50 for all the simulations (see Ref. [17] for details). For Case II, the mesh generated for the 2D case is extruded to finite unit length. The same zonal approach is used; now the inner rotor cylinder is surrounded by a cube of outer domain. The same mesh topology is maintained for all the cases. The 3D finite length mesh, with symmetric boundary conditions, does not have the supporting arms, central shaft and central disc. These simulations are then followed by extending the boundary away from the blades to include tip effects, termed as Case III. In Case IV, we include the supporting arms and central disc assembly for Case II, i.e. no tip effects. In Case V, we employ the model to simulate the flow past an actual turbine with supporting arms, central disc, and central shaft assembly plus tip effects. Fig. 2 provides a view of the mesh for all the cases. 2.2. Flow field setup The left side of the domain is the velocity-inlet boundary with turbulent intensity of 10% and length scale of 0.01 m. At outlet boundary on the right, all the flow properties except pressure are
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Table 1 Details of geometric approximation of a turbine Model.
extrapolated from the flow field while an outflow pressure is fixed and the top and bottom boundaries are assigned as the far field boundary conditions. No-slip boundary condition is specified at the blade and the supporting surfaces. This causes the relative velocity to be zero at the wall. The rotor zone which includes the turbine blade and is supposed to rotate during the transient solution is considered as the sliding zone and assigned the interface boundary condition. For the three-dimensional mesh, the upper and lower
faces were defined as the symmetry boundary conditions. The density-based solver is chosen with the second-order accurate spatial discretization. For gradients control, Green Gauss Cell Based scheme is used. The under relaxation factors for the turbulent kinetic energy, turbulent dissipation rate, and turbulent viscosity are set at 0.8, 0.8, and 1.0, respectively. The details of the applied boundary conditions can be found in the ANSYS Fluent© User Manual.
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Fig. 2. Zoom-in view of the grid on various structural configurations of the VAWT.
Fig. 3 shows a cross-section of the blade (airfoil) traversing one complete rotation along upwind (0 e180 ) and downwind (180 e360 ) regions with free incoming wind velocity (U). As a keeps on increasing, the lift begins to increase which must be perpendicular to the relative wind velocity direction. This induced
Fig. 3. Relative velocities and forces acting on a rotating blade along upwind (0 e180 ) and downwind (180 e360 ) side.
lift is responsible for the counter-clockwise rotation of the blade and drives the VAWT blades. The relative speed varies from 0 m/s to 85 m/s for the wind velocity of 12 m/s. Hence to the changing relative velocity the local Reynolds number at the blades changes during the rotation. For one complete rotation of blades the Reynolds number based on the chord length is evaluated to be in the limits of 70,000
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2.3. Important parameters For wind turbines, tip speed ratio is defined as the ratio between the rotation (u) of the tip of a blade and the actual wind velocity (Vw). If the velocity of the tip is exactly the same as the wind speed the tip speed ratio is unity. Mathematically,
TSR ¼
Ru Vw
(1)
Other performance parameters include the torque ripple and overall torque. The torque ripple is the torque generated by a single blade during the rotation. An important parameter for the wind turbine is the performance coefficient (Cp) which is a measure of turbine efficiency. It signifies how efficient the turbine is in extracting the power available in the wind. It is defined as
PT ¼ Tu n
PW ¼ Cp ¼
1 As V3w 2
PT Pw
(2)
(3)
(4)
where As is the swept area of the rotor, PT is the power extracted by the VAWT, and Pw is the power available in the wind. Since the extracted power can never be greater than the power available in the wind, thus theoretically its value should be between 0 and 1. But the Betz law [18] predicts that ideally its value could never be greater than is 59.7% which is also known as Betz limit. Thus, no turbine practically should have the value of performance coefficient more than 59.7%. 3. Numerical simulations We numerically simulate all the Cases in Table 1 and compute the torque ripple, overall torque, and the performance coefficient. Comparing the performance parameter, we quantify the effects of each structural component in the VAWT design under consideration. As a sample case, we numerically validate and verify the variation of performance parameters for Case I at TSR magnitude of 3. This choice of TSR equal 3 is motivated by the fact that performance coefficient is maximum for all cases, discussed later in the present study. For validation, numerical results are compared with those available in the literature; both numerical and experimental. In order to verify the results, various studies are conducted, such as grid independence, time independence, turbulence model, and spatial discretization [17]. In this study, K-ε Realizable model is used for turbulence modeling. The convergence criterion for all the parameters is set to 1E-4, especially the continuity equation. Lift coefficient, drag coefficient, and moment coefficient are observed until they start to oscillate about a mean value. The solution gets converged by iterating at every time step before moving to the next time step. During the start of the simulations, instability due to mixing of incoming flow and rotating mesh occurred. It is due to convergence difficulties of second-order upwind scheme. To overcome this problem, first-order upwinding is employed during the starting-up flow instability. Once the solution becomes periodic, second-order upwind discretization is employed. Fig. 4 shows the torque ripple plot over seven cycles. The starting instability is observed in the initial stage. Several revolutions need to be formulated before a periodic solution is obtained.
Torque (Nm)
Transient soluƟon 60 50 40 30 20 10 0 -10 -20 -30 -80 -40
665
Periodic soluƟon Airfoil1
280
640
1000 1360 1720 Azimuth angle (deg)
2080
2440
2800
Fig. 4. Periodic torque ripple result over seven rotations of turbine.
The fluctuating trend in the torque ripple curve at a particular TSR value can also be explained through pressure contours plotted in Fig. 5. The contour level are set at the same level to compare pressure intensity at q ¼ 0 , 90 , 180 , and 270 . We can observe that the pressure intensity is higher while comparing q ¼ 0 and 180 . Similarly, flow separation region is more negative for q ¼ 90 than that of 270 which corresponds to higher pressure difference leading to more torque generation. In terms of effective angle of attack at q ¼ 0 , the blade chord makes zero angle of attack with the relative velocity. Since symmetrical airfoils are employed, they result in no lift force at zero a. Thus, no component of force contributes in the tangential direction which causes the torque to be zero at this point. With the increase of azimuth angle, a also increases. This rise in a causes the lift force to increase due to which the magnitude of the torque becomes more positive. Near q ¼ 90 , the airfoil makes critical a, thus a peak in torque value is observed. Once the peak torque is reached, the blade enter stall and loses lift resulting in low torque values. As the airfoil reaches q ¼ 180 , again the torque goes back to zero as there is no effective a. During the path from q ¼ 180 to q ¼ 360 , a again increases to its critical value. But flow disturbance due to large vortices in the downwind path and the fact that the energy was already extracted in the upwind path, the blades contributes small towards the positive torque values. We simulate the flow past 2D turbine on three different meshes; 70,000 cells (coarse grid), 78,000 cells (baseline grid), and 86,000 cells (finer grid). Fig. 6(a) plots the torque ripple on the three grid sizes. We observe that, on the coarser grid, the magnitude of torque ripple decreases by approximately 40% as compared to that obtained on the baseline grid. As the grid size is made finer, the magnitude of the torque ripple stays within 5% of its magnitude, thus providing confidence on the baseline grid. Cases II & III have the same mesh topology as in Case I. For Case IV, the complete turbine case, the generated mesh contained over 2 million cells. The results from the baseline mesh (2,200,000 cells) are compared to a finer mesh (3,300,000 cells) and a coarser mesh (1,400,000 cells). We also used a Gridgen mesh (2,000,000 cells) to verify the accuracy of our numerical results. The coarser mesh shows a significant difference in results while the results of similar magnitude are obtained from the finer mesh (see Fig. 6(b)). The numerical accuracy is also verified by comparing the results with the results obtained from the Gridgen mesh. The size selected after grid independence gives consistent numerical predictions even if the mesh size is further improved. So, in order to economize the computational cost, the mesh with lower size is chosen which gives no appreciable deviations of results when more finer mesh is used. The plots of torque ripple from both the meshes show that results stay within 5% bounds, thus verifying the accuracy of our numerical solution.
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Fig. 5. Pressure contours at q¼0 (top left), 90 (left bottom), 180 (right bottom), and 270 (right top).
The justification for selection of different parameters such as time step and turbulence model etc. can be found in our previous work [18]. 4. Numerical results & analysis
produces higher torque during the upwind path as compared to the torque in the downwind path. It is interesting to note that at lower magnitude of TSR equal to 1.5, there is a dip (marked with dotted circular lines) in the secondary peak observed in the torque ripple which diminishes as the TSR magnitude is increased. We attribute this dip to the vortices
In this Section, we analyze the numerical results obtained for all Cases. We perform numerical simulations over a range of TSR magnitude of 1.5 till 4.5 with an increment of 0.5 to observe the variation turbine performance with changing rpm. For visualization of the flow field, we plot magnitude of the vorticity contours for the Cases III, IV and V in Fig. 7. These flow field structures due to different geometric design approximated for a VAWT affect the performance of the turbine. Detailed vorticity contours over a complete cycle can be found in Ref. [18]. In this study, we restrict our discussion to the performance parameters for different configurations of VAWT highlighting the effect of geometric approximations. We discuss torque ripple and overall torque for Case I in detail for complete range of TSR from 1.5 till 4.5 with an increment of 0.5. Similar trends are observed for other cases due to which torque ripple is plotted for remaining the Cases in Fig. 9. 4.1. Case I We plot the torque ripple and the overall torque magnitudes in Fig. 8 for TSR 1.5, 3.0, and 4.5. For the torque ripple, we observe two peaks for a complete revolution of a turbine blade. Sharp peak is produced in the torque ripple as the blade traverses the upwind region near q ¼ 90 when the relative angle of attack is maximum while a smaller peak is produced as the blade is around q ¼ 270 . The secondary peak is attributed to the wake generated by the blade during the upwind path reducing the relative velocity as the blade traverses the downwind path. In other words, the blade
Fig. 6. Grid independence study for (a) Case I and (b) Case IV.
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4.2. Case II The torque ripples at all the TSR values are combined together in a single plot as shown in Fig. 9(b). The overall trend remains the same. This is also expected because Case II is mere extension of 2D blade to form the unit span length of the wing with symmetric boundary conditions at the end. The maximum values of both positive and negative torques are generated for higher TSR values with the high positive torques on the upwind side and less negative values during the downwind path of the rotation. 4.3. Case III Tip effects are the very critical phenomenon which is usually shed from the airfoils type blades. Air from the bottom with high pressure tends to reach the lower pressure air on the top of the wing surface, this air movement is considered to be span wise flow that means it is spreading over the wing and the only point to reach the low pressure air region is flowing over the wing tip. In order to see the tip effects from the blades the domain is extended in the z direction (See Fig. 2(c)). Thus, the rotor region is completely surrounded by the outer domain. The domain is extended adequately so the boundary does not have any effect on the flow physics of the blades. The results are formulated over the range of tip speeds in Fig. 9(c). Due to the addition of tip effects, strong wing tip vortices are generated which reduce the aerodynamic lift and cause a substantial increase in the drag force which degrades the power output of the turbine. 4.4. Case IV
Fig. 7. Instantaneous vorticity contours plotted for three-dimensional configurations of the turbine.
shed by a turbine blade, around q ¼ 90 , convect through the wake and interact with the same blade when it reaches q ¼ 270 . It is established by comparing the time scales of vortex convecting through a distance equal to the diameter of the turbine with approximately 12 m/s, i.e. 2.5/12 ¼ 0.208 s. At TSR ¼ 1.5, angular velocity can be computed from Equation (1) as 14.4 rad/sec which corresponds to approximately 825 /sec (or 2.29 revolutions/sec). Thus, half revolution (q ¼ 90 to 270 ) would take around 0.218 s for a blade to traverse this distance. In order to make a comparative analysis of the performance of a turbine at different rpm (TSR), we plot cumulative torque over the range of rpm in the right column of Fig. 8. It depicts the performance gains and drops of the turbine with the changing rotational speeds. In general, the torque increases with the increase in TSR. We observe maximum magnitude of torque ripple for TSR ¼ 4.5. However, we also observe negative torque for the same TSR magnitude. It can be attributed to high rotational speed and, with sliding mesh method, are non physical. The torque ripple for all TSR cases are superimposed in Fig. 9(a) and compared with other cases.
The addition of the support arms, central shaft and hub results in low torque generation over the cycle for a TSR value as shown in Fig. 9(d). It appeared that it produced negative overall torques at high TSR values. In comparison to Case II (without central assembly), the torque ripple curve experience more negative torque while the blades are moving through the downwind path specifically between q ¼ 220 to q ¼ 360 . It is because of the effect of span wise flow, blade-tips and additional profile drag due to support arms and central hub assembly. Also, the effect is contributed to the extra drag and strong vortices generation with the addition of the extra assembly. The contours of vorticity magnitude further the explanation of the negative torques as a sudden rise in turbulent intensities, extra profile drags and increased vorticity has been observed with the addition of support arms and hub. 4.5. Case V A number of significant differences are observed for the complete turbine model case in comparison to the 2D case. Although, torque generation between the two cases is qualitatively similar, the average torque of 3D experienced a drop of 32% in comparison to that of 2D case. The simulated torque ripples at different TSR values are superimposed in Fig. 9(e) to determine the effect on the changing rpm on the performance. More momentous difference is observed in the downwind path than in the upwind. Positive torques are only produced between 210
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Fig. 8. Torque ripple (left column) and overall torque (right column) for Case I.
energy from the wind. It causes a substantial rise in both resistive loads and the drag friction. Thus, negative performance coefficients are observed for the turbines at high TSR (numerically). Practically, the turbine will slow down under the influence of the resistive loads.
It is interesting to observe that the magnitude of torque ripple in the upward region peaks around the same location whereas the location varies in downward side. It is mainly due to the flow disturbance generated in the wake of the blade varies for each Case. This disturbance convects and affects the torque ripple in the downward side.
5. Parametric quantification of geometric approximations 5.2. Overall torque In this section, we compare the performance parameters for all the Cases and quantify the effects of geometric approximations of a given VAWT design. We can thus identify the contribution of each component in the overall performance. Another aspect of these analyses is to optimize the VAWT design by performing numerical simulations through approximate design which can fairly depict complete turbine design. 5.1. Torque ripple We plot one complete cycle of torque ripple for all Cases at the TSR of 3 in Fig. 10. It is evident from the plots that the torque ripple follows a similar overall trend; however, its magnitude varies according to the case. As expected, Case I over predicts the torque ripple values as compared to all the 3D Cases IIeV. The addition of third dimension and support structure cause flow obstructions and vortices which degrades the torque ripple. The drop is more during the downwind side as compared to upwind.
The next parameter evaluated from the numerical results is the overall torque for all the Cases. Since the overall torque is the combined effect of all the blades, it is strongly affected by individual torque ripples. The overall torque at the TSR of 3 is plotted in the Fig.11. Again, Case I results in the maximum value. The addition of third dimension and support structure affect spanwise flow, tip vortices and cause additional profile drag which reduce the overall torque. Thus, the overall torque decreases as we move from Case I to Case V. We also note that the overall torque goes negative for Case V. It means that a complete 3D VAWT will cease to operate contribute positively when the rotational crosses a certain thresh hold value. It is because the rotor blades will be rotating so fast that a possible stagnant localized zone will be generated in the rotor region. It will decelerate the rotating blades and extracted energy will go down to zero. However, since in CFD solution, a TSR value is forced. Hence, it is not possible to capture this dynamics and instead a negative performance coefficient is depicted.
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(a)
(b)
Fig. 10. One torque ripple cycle for different cases.
5.3. Performance coefficient
(c)
(d)
The performance coefficient shows a decrease in performance from Case I to Case V. The results are plotted in Fig. 12. The maximum value for Case I is around 0.5. For all the cases the performance coefficient curves starts with a lower value reaches a maximum value (at TSR ¼ 3) and drops to lower values. One important observation is the sudden drop in performance of the turbine with support structure at high rpm. This is because of the whirlpool effect the turbine experience at high rpm. The blade starts to rotate so fast that they do not properly interact with on coming air resulting in a substantial decrease in the performance. As we have forced the rotation to the rotor region, thus this effect is only numerical. It is also interesting to note that performance coefficients in Case II and III follow each other very closely. In other words, the tip effects are minimal in computing the overall turbine power. Similarly, Cases IV and V indicate that the effect of structural components is dominant as compared to the tip effects. Inclusion of support arm, central hub and shaft decreases the overall performance coefficient. The results for all five cases are also quantified in Table 2. As indicated earlier that Case I over predicted the torque values. To quantify the decrease in the performance, we compute the relative difference and term it “geometric” error due to structural approximations. In physical sense, it is the over prediction of twodimensional simulations lacking third dimensional flow. Fig. 13 plots the percentage drop in the performance for the Cases relative to Case I. We find that a percentage drop in performance of 18%
(e)
Fig. 9. Comparison of torque ripple for (a) Case I, (b) Case II, (c) Case III, (d) Case IV and (e) Case V.
Fig. 11. Overall torque for one complete rotation.
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Fig. 13. Percentage drop in power relative to Case I (2D).
Fig. 12. Power coefficient for different cases.
is expected from simple 2D (Case I) to simple 3D (Case II) simulations. By addition of tip effects from the blades (Case III) an additional 3% drop is observed. Further incorporating the three dimensional support structures (Case IV) the overall drop jumps to 26% relative to the 2D analysis. With the addition of tip effects in the support structure (Case V) the drop reaches to 32%. Usually researchers exclude the support structure (support arms and central hub) to focus on VAWT blades only, thus they should expect approximated error of 10%e12%. Practically, the results of Case V are expected to be in close agreement with the real-time results as they have the highest level of complexity with lower approximations. 6. Conclusion A detailed insight of the flow physics of VAWT is presented. Torque ripple at different conditions is explained. It can be concluded that it is very important to quantify and understand the effect of various levels of approximations done in CFD simulations. This finding high lights the fact that care must be taken in drawing conclusions based on pure 2D simulations, or simulations with no tip effects for performance of any VAWT. This study gives an overview of possible error in predictions due to various approximations. The optimum performance of a VAWT depends on its rotational speed. In present study, it is found at a TSR value of 3. A simulation done in 2D can over predict the performance up to 32 percent in comparison with real time 3D CFD simulation. The support structure of the under consideration VAWT consists of the supporting arms, central hub and the shaft. If we neglect the support structure in 3D simulations (only blades), then the tip effects can cause a difference of upto 3% in performance coefficient prediction. However, if the support structure is considered in the 3D simulations, the tip effects can cause upto 6%. The difference of results from 3D (blades only) and complete 3D with support structure; both with the tip effects is computed as
Table 2 Cp vs TSR for all Cases. TSR
Case I
Case II
Case III
Case IV
Case V
1.5 2 2.5 3 3.5 4 4.5
0.191 0.29 0.423 0.51 0.458 0.347 0.122
0.159 0.265 0.353 0.415 0.381 0.289 0.102
0.165 0.265 0.353 0.415 0.381 0.289 0.102
0.145 0.245 0.324 0.343 0.305 0.191 0.091
0.161 0.261 0.342 0.361 0.311 0.201 0.073
11%. These finding high lights the fact that care must be taken in drawing conclusions based on pure 2D simulations, or simulations with no tip effects for performance of any VAWT. This study gives an overview of possible error in predictions due to various approximations. References [1] Bhutta M.M.A, Hayat N., Farooq A.U., Ali Z., Jamil S.R., Hussain Z., Vertical axis wind turbine e a review of various configurations and design techniques. Renew Sustain Energy Rev; Vol. 16, pp. 1926e1939. [2] Hamada K, Smith TC, Durrani N, Qin N, Howell RJ. Unsteady flow simulation and dynamic stall around vertical axis wind turbine blades. In: AIAA-20081319, 46th AIAA aerospace sciences meeting and exhibit, Reno, Nevada; Jan. 7e10, 2008. [3] Durrani N, Hameed H, Rahman H, Chaudhry SR. A detailed aerodynamic design and analysis of a 2D vertical axis wind turbine using sliding mesh in CFD. In: 49th AIAA aerospace sciences meeting; 4e7 January 2011. Orlando, Florida, USA. [4] Durrani N, Qin N, Hameed H, Khushnood S. Comparison of a single stage and multistage vertical axis wind turbines using sliding mesh in 2D. In: AIAA2011-541, 49th AIAA aerospace sciences meeting; 4e7 January 2011. Orlando, Florida, USA. [5] Hwang IS, Hwang CS, Min SY, Jeong IO, Lee YH, Kim SJ. Efficiency improvement of cycloidal wind turbine by active control of blade motion. In: 16th international conference on adaptive structures and technologies; 9e12 October 2005. Paris, France. [6] Ferreira CS, Bussel GV, Kuil GV. 2D CFD simulation of dynamic stall on a vertical axis wind turbine: verification and validation with PIV measurements. In: 45thAIAA aerospace sciences meeting and exhibit; 8e11 January 2007. Reno, Nevada, USA. ~ ada: DCW Industries; [7] Wilcox CD. Turbulence modeling for CFD. 2nd ed. La Can 1998. [8] Eriksson S., Bernhoff H., Leijon M., Evaluation of different turbine concepts for wind power. Renew Sustain Energy Rev; Vol. 12, pp. 1419e1434. [9] Marini M., Massardo A., Satta A., Performance of vertical axis wind turbines with different shapes. J Wind Eng Indus Aerodynamics, Vol. 39, pp. 83e93. [10] Brahimi M.T., Allet A., Paraschivoiu I., Aerodynamic analysis models for vertical-Axis wind turbines. Int J Rotating Mach; Vol. 2, pp. 15e21. [11] Claessens MC. The design and testing of airfoils for application in small vertical axis wind turbines. MSc Thesis. Delft University of Technology, Faculty of Aerospace Engineering; 2006. [12] Timmer WA, van Rooij RPJOM. Summary of the Delft university wind turbine dedicated airfoils. AIAA-2003-0352. 2003. [13] Hamada K, Smith TC, Durrani N, Qin N, Howell RJ. Unsteady flow simulation and dynamic stall around vertical axis wind turbine blades. In: AIAA aerodynamics conference; 7e10 January 2008. Reno, Nevada, USA. [14] Edwards J, Durrani N, Howell R, Qin N. Wind tunnel and numerical study of a small vertical axis wind turbine. In: AIAA 27th ASME wind Energy symposium, 7e10 January 2008; 2007. Reno, Nevada, USA. [15] Howell R., Qin N., Edwards J. and Durrani N., Wind tunnel and numerical study of a small vertical axis wind turbine, Renew Energy; Vol. 35, pp. 412e422. [16] Qin N., Howell R., Durrani N., Hamada K. & Smith T., Unsteady flow simulation and dynamic stall behavior of vertical axis wind turbine. Wind Eng, Vol; 35, pp. 425e449. [17] Siddiqui MS, Durrani N, Akhtar I. numerical study to quantify the effects of struts & central hub on the performance of a three dimensional vertical axis wind turbine using sliding mesh. In: ASME 2013 power conference; 2013. p. 11. http://dx.doi.org/10.1115/POWER2013-98300. Paper No. POWER2013e98300. o A. Wind power distributions: a review of their applica[18] Villanueva D, Feijo tions. Renew Sustain Energy Rev 2010;14(5):1490e5.
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Quantification of the effects of geometric approximations on the performance of a vertical axis wind turbine M. Salman Siddiqui, Naveed Durrani 1, Imran Akhtar*, 2 Department of Mechanical Engineering, NUST College of Electrical & Mechanical Engineering, National University of Sciences & Technology, Islamabad 44000, Pakistan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 December 2013 Accepted 24 August 2014 Available online
With the soaring energy demands, an urge to explore the alternate and renewable energy resources has become the focal point of various active research fronts. The scientific community is revisiting the inkling to tap the wind resources in more rigorous and novel ways. Recent idea of net-zero buildings has prompted the realization of novel ideas such as employment of omni-directional vertical-axis wind turbine (VAWT) for roof-top application etc. Generally, owing to the high computational cost and time, different levels of geometric simplifications are considered in numerical studies. It becomes very important to quantify the effect of these approximations for realistic and logical conclusions. The detailed performance of a 2.5 m diameter VAWT is sequentially presented with various levels of approximations spanning from two-dimensional to complete three-dimensional geometry. The performance along with the flow physics with focus on tip effects, spanwise flow effects, effect of supporting arms and central hub is discussed. We conclude that two-dimensional approximation can over predict the performance by 32%. Similar trend is also observed for other geometric and flow approximations. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Vertical-axis wind turbine Geometric approximation Performance parameter Numerical simulation Sliding mesh
1. Introduction A substantial shift towards promoting the renewable energy is evident with the growing awareness of environmental pollution. Concerns about the global warming and depleting reserves of fossil fuels have further strengthened the drive to explore the alternative energy venues. Consequently, a revitalized interest in different related areas such as power generation through windmills is observed around the globe. One particular area in focus is about the suitability of using wind turbines to generate power in an urban environment. The idea to place a wind turbine on top of buildings may seem less than ideal as a first thought. This application has received considerable attention in net-zero building design. Nevertheless, the expected benefits in terms of clean and green power output have attracted a sizeable scientific community to explore this idea. Flow of air around a wind turbine housed over a building in a built up area requires consideration of different
* Corresponding author. E-mail address: [email protected] (I. Akhtar). 1 Visiting Faculty, Institute of Space Technology, Islamabad, Pakistan. 2 Also Adjunct Research Member, Interdisciplinary Center for Applied Mathematics, MC 0315, Virginia Tech, Blacksburg, VA 24061, USA. http://dx.doi.org/10.1016/j.renene.2014.08.068 0960-1481/© 2014 Elsevier Ltd. All rights reserved.
factors. These factors include variation in turbulence intensity and wind shear, change of direction of wind and distance of blades from the ground etc. Wind turbines are classified by their axis of rotation into two general types: horizontal axis wind turbine (HAWT) a vertical axis wind turbine (VAWT). Recently VAWT has received considerable attention due to inherent characteristics of omni-directionality, less noise, simplicity of manufacturing, mechanically able to withstand higher wind speeds and their efficiency when put on the urban rooftop building have revived the interest in VAWT. The flow physics is expected to be complex due to wake with flow structures of different length scales, high directional variability, large skew angles and increased turbulence intensity. To design an optimum configuration under various flow conditions, computational fluid dynamics (CFD) provides an affordable and a practical tool simulate the flow around the VAWT. Despite all the advancements in computer architecture and numerical methods, an exact computational fluid dynamic analysis, also termed as direct numerical simulation (DNS) is not possible. So, the simulations have to be limited by accepting approximations in conjunction with the desired level of accuracy and available computational time and cost resources. The challenges involve in the simulation include the rotational aspect of the rotor blades and ensuing vortex shedding, effect of central shaft and hub on the flow
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and wakeerotor interactions etc. Different geometric approximations are generally considered to do the numerical simulations of this highly complex rotating turbine cases. The flow governing equations are generally approximated using Reynolds-averaged Navier Stokes (RANS) for real time 3D flows due to their reasonable relative accuracy with less computational time. In literature, limited research work is available regarding the detailed aerodynamic analysis of VAWT using the CFD analysis. For detailed review of various configurations and design techniques of the VAWT, readers are referred to Ref. [1]. Hamada et al. [2], Durrani et al. [3,4] performed numerical analysis on a horizontal (H)-VAWT to study its aerodynamics. They analyzed the flow field and compared various blade profiles to determine the effect of blade thickness, blade fixing angle, thickness, camber effects and dynamic stall on the overall performance. Hwang [5] employed a commercial CFD package; (STAR-CD) for the performance predictions of the VAWT. He performed moving mesh analysis using the k-3 turbulence model. Ferreira et al. [6] investigated effects of different turbulence models, such as one equation SpalartAllmaras (S-A) model [7], on the flow field. Eriksson et al. [8] and Marini et al. [9] performed the aerodynamic analysis of the Darrieustype wind turbine. They also discussed different configurations of the VAWT and compared their effect on performance parameters. Brahimi et al. [10] developed a numerical algorithm known as “TKFLOW”. Results using TKFLOW could predict the region where the dynamic stall might occur. Claessens [11] performed the study to improve the performance of the NACA 0018 profile. He used the commercial tool RFOIL [12] and developed a numerical algorithm for the calculation of VAWT performance parameters. He proposed his own design of an airfoil and named it DU 06-W-200. He predicted that the proposed airfoil has increased structural strength, enhanced torque generation in the downwind path and results in smaller drop in lift coefficients as compared to the other airfoils. In this paper, we extend and build on the existing studies [13e15] on the performance of the VAWT. With recent advances in computing technology and available CFD software, it has become viable to conduct full scale simulations of the complete turbine. However, it is still not feasible to perform a complete set of simulations over a wide parametric range for multidisciplinary design optimization. Thus, researchers often resort various approximations on actual 3D VAWT. These approximations can be a simple 2D analysis, 3D analysis with top and bottom symmetry, i.e. infinite span with no tip effects, and 3D analysis with finite span including tip effects. In 3D analysis, some researchers exclude the support structure (support arms and central hub) to focus on VAWT blades only. Hence, it becomes very important to understand and quantify the effects of geometric approximation on turbine performance. Thus, the key objective of this work is to quantify the effects of different approximations employed in CFD analysis for a fixed VAWT design. In other words, we explore how good the 2D or 3D analysis to compute its performance parameters is. The quantification employs comparison of parameters torque ripple, overall torque, and the performance coefficient over a range of tip-speed ratio. 2. The computational model and setup 2.1. Geometric model The type of wind turbine in the present study is a fixed pitch straight blade Darrieus type H-VAWT as shown in Fig. 1. The turbine has a diameter of 2.5 m with 0.2 m chord length and blade length (span) of 2.5 m. Thus, the aspect ratio is 12.5 with no taper. We select NACA 0022 airfoil based on the previous work [14]. The baseline inlet velocity is 12 m/s for all the cases. The rated power output is expected to be around 2 KW.
Fig. 1. CAD model of 3-bladed H-VAWT with support arm and struts.
In order to numerically simulate the flow past the turbine, we generate the mesh using Gambit and then export it into the ANSYSFLUENT solver. Various geometric configurations to approximate VAWT design are tabulated in Table 1. We consider five cases ranging from a two-dimensional airfoil to a complete turbine model. Details of the grid points and simulation time per iteration are also provided. In the last column, a schematic of each case is shown to elaborate geometric approximation of the turbine model. Brief description of each case is also provided for better apprehension of the reader. For Case I, a 2D model of the turbine, comprising three airfoils (blades) 120 apart, is created. The support arms, central shaft and the disc are not incorporated in Case I. The domain size is set as 50c 30c (where c is the chord length), motivated by the fact that this domain size does not affect on the flow behavior of the rotating turbine [16]. The rotor computational domain is located at the center of the domain space. In order to enhance the quality of mesh generation, we employ a zonal approach. We create two computational domains; the rotor domain and the outer domain which are then connected together through “interfaces”. Tri-diagonal mesh concept is employed and the boundary layer and size function are used to generate a clustered mesh near airfoils. It helps in capturing the flow physics adequately. The yþ values kept under 50 for all the simulations (see Ref. [17] for details). For Case II, the mesh generated for the 2D case is extruded to finite unit length. The same zonal approach is used; now the inner rotor cylinder is surrounded by a cube of outer domain. The same mesh topology is maintained for all the cases. The 3D finite length mesh, with symmetric boundary conditions, does not have the supporting arms, central shaft and central disc. These simulations are then followed by extending the boundary away from the blades to include tip effects, termed as Case III. In Case IV, we include the supporting arms and central disc assembly for Case II, i.e. no tip effects. In Case V, we employ the model to simulate the flow past an actual turbine with supporting arms, central disc, and central shaft assembly plus tip effects. Fig. 2 provides a view of the mesh for all the cases. 2.2. Flow field setup The left side of the domain is the velocity-inlet boundary with turbulent intensity of 10% and length scale of 0.01 m. At outlet boundary on the right, all the flow properties except pressure are
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Table 1 Details of geometric approximation of a turbine Model.
extrapolated from the flow field while an outflow pressure is fixed and the top and bottom boundaries are assigned as the far field boundary conditions. No-slip boundary condition is specified at the blade and the supporting surfaces. This causes the relative velocity to be zero at the wall. The rotor zone which includes the turbine blade and is supposed to rotate during the transient solution is considered as the sliding zone and assigned the interface boundary condition. For the three-dimensional mesh, the upper and lower
faces were defined as the symmetry boundary conditions. The density-based solver is chosen with the second-order accurate spatial discretization. For gradients control, Green Gauss Cell Based scheme is used. The under relaxation factors for the turbulent kinetic energy, turbulent dissipation rate, and turbulent viscosity are set at 0.8, 0.8, and 1.0, respectively. The details of the applied boundary conditions can be found in the ANSYS Fluent© User Manual.
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Fig. 2. Zoom-in view of the grid on various structural configurations of the VAWT.
Fig. 3 shows a cross-section of the blade (airfoil) traversing one complete rotation along upwind (0 e180 ) and downwind (180 e360 ) regions with free incoming wind velocity (U). As a keeps on increasing, the lift begins to increase which must be perpendicular to the relative wind velocity direction. This induced
Fig. 3. Relative velocities and forces acting on a rotating blade along upwind (0 e180 ) and downwind (180 e360 ) side.
lift is responsible for the counter-clockwise rotation of the blade and drives the VAWT blades. The relative speed varies from 0 m/s to 85 m/s for the wind velocity of 12 m/s. Hence to the changing relative velocity the local Reynolds number at the blades changes during the rotation. For one complete rotation of blades the Reynolds number based on the chord length is evaluated to be in the limits of 70,000
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2.3. Important parameters For wind turbines, tip speed ratio is defined as the ratio between the rotation (u) of the tip of a blade and the actual wind velocity (Vw). If the velocity of the tip is exactly the same as the wind speed the tip speed ratio is unity. Mathematically,
TSR ¼
Ru Vw
(1)
Other performance parameters include the torque ripple and overall torque. The torque ripple is the torque generated by a single blade during the rotation. An important parameter for the wind turbine is the performance coefficient (Cp) which is a measure of turbine efficiency. It signifies how efficient the turbine is in extracting the power available in the wind. It is defined as
PT ¼ Tu n
PW ¼ Cp ¼
1 As V3w 2
PT Pw
(2)
(3)
(4)
where As is the swept area of the rotor, PT is the power extracted by the VAWT, and Pw is the power available in the wind. Since the extracted power can never be greater than the power available in the wind, thus theoretically its value should be between 0 and 1. But the Betz law [18] predicts that ideally its value could never be greater than is 59.7% which is also known as Betz limit. Thus, no turbine practically should have the value of performance coefficient more than 59.7%. 3. Numerical simulations We numerically simulate all the Cases in Table 1 and compute the torque ripple, overall torque, and the performance coefficient. Comparing the performance parameter, we quantify the effects of each structural component in the VAWT design under consideration. As a sample case, we numerically validate and verify the variation of performance parameters for Case I at TSR magnitude of 3. This choice of TSR equal 3 is motivated by the fact that performance coefficient is maximum for all cases, discussed later in the present study. For validation, numerical results are compared with those available in the literature; both numerical and experimental. In order to verify the results, various studies are conducted, such as grid independence, time independence, turbulence model, and spatial discretization [17]. In this study, K-ε Realizable model is used for turbulence modeling. The convergence criterion for all the parameters is set to 1E-4, especially the continuity equation. Lift coefficient, drag coefficient, and moment coefficient are observed until they start to oscillate about a mean value. The solution gets converged by iterating at every time step before moving to the next time step. During the start of the simulations, instability due to mixing of incoming flow and rotating mesh occurred. It is due to convergence difficulties of second-order upwind scheme. To overcome this problem, first-order upwinding is employed during the starting-up flow instability. Once the solution becomes periodic, second-order upwind discretization is employed. Fig. 4 shows the torque ripple plot over seven cycles. The starting instability is observed in the initial stage. Several revolutions need to be formulated before a periodic solution is obtained.
Torque (Nm)
Transient soluƟon 60 50 40 30 20 10 0 -10 -20 -30 -80 -40
665
Periodic soluƟon Airfoil1
280
640
1000 1360 1720 Azimuth angle (deg)
2080
2440
2800
Fig. 4. Periodic torque ripple result over seven rotations of turbine.
The fluctuating trend in the torque ripple curve at a particular TSR value can also be explained through pressure contours plotted in Fig. 5. The contour level are set at the same level to compare pressure intensity at q ¼ 0 , 90 , 180 , and 270 . We can observe that the pressure intensity is higher while comparing q ¼ 0 and 180 . Similarly, flow separation region is more negative for q ¼ 90 than that of 270 which corresponds to higher pressure difference leading to more torque generation. In terms of effective angle of attack at q ¼ 0 , the blade chord makes zero angle of attack with the relative velocity. Since symmetrical airfoils are employed, they result in no lift force at zero a. Thus, no component of force contributes in the tangential direction which causes the torque to be zero at this point. With the increase of azimuth angle, a also increases. This rise in a causes the lift force to increase due to which the magnitude of the torque becomes more positive. Near q ¼ 90 , the airfoil makes critical a, thus a peak in torque value is observed. Once the peak torque is reached, the blade enter stall and loses lift resulting in low torque values. As the airfoil reaches q ¼ 180 , again the torque goes back to zero as there is no effective a. During the path from q ¼ 180 to q ¼ 360 , a again increases to its critical value. But flow disturbance due to large vortices in the downwind path and the fact that the energy was already extracted in the upwind path, the blades contributes small towards the positive torque values. We simulate the flow past 2D turbine on three different meshes; 70,000 cells (coarse grid), 78,000 cells (baseline grid), and 86,000 cells (finer grid). Fig. 6(a) plots the torque ripple on the three grid sizes. We observe that, on the coarser grid, the magnitude of torque ripple decreases by approximately 40% as compared to that obtained on the baseline grid. As the grid size is made finer, the magnitude of the torque ripple stays within 5% of its magnitude, thus providing confidence on the baseline grid. Cases II & III have the same mesh topology as in Case I. For Case IV, the complete turbine case, the generated mesh contained over 2 million cells. The results from the baseline mesh (2,200,000 cells) are compared to a finer mesh (3,300,000 cells) and a coarser mesh (1,400,000 cells). We also used a Gridgen mesh (2,000,000 cells) to verify the accuracy of our numerical results. The coarser mesh shows a significant difference in results while the results of similar magnitude are obtained from the finer mesh (see Fig. 6(b)). The numerical accuracy is also verified by comparing the results with the results obtained from the Gridgen mesh. The size selected after grid independence gives consistent numerical predictions even if the mesh size is further improved. So, in order to economize the computational cost, the mesh with lower size is chosen which gives no appreciable deviations of results when more finer mesh is used. The plots of torque ripple from both the meshes show that results stay within 5% bounds, thus verifying the accuracy of our numerical solution.
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Fig. 5. Pressure contours at q¼0 (top left), 90 (left bottom), 180 (right bottom), and 270 (right top).
The justification for selection of different parameters such as time step and turbulence model etc. can be found in our previous work [18]. 4. Numerical results & analysis
produces higher torque during the upwind path as compared to the torque in the downwind path. It is interesting to note that at lower magnitude of TSR equal to 1.5, there is a dip (marked with dotted circular lines) in the secondary peak observed in the torque ripple which diminishes as the TSR magnitude is increased. We attribute this dip to the vortices
In this Section, we analyze the numerical results obtained for all Cases. We perform numerical simulations over a range of TSR magnitude of 1.5 till 4.5 with an increment of 0.5 to observe the variation turbine performance with changing rpm. For visualization of the flow field, we plot magnitude of the vorticity contours for the Cases III, IV and V in Fig. 7. These flow field structures due to different geometric design approximated for a VAWT affect the performance of the turbine. Detailed vorticity contours over a complete cycle can be found in Ref. [18]. In this study, we restrict our discussion to the performance parameters for different configurations of VAWT highlighting the effect of geometric approximations. We discuss torque ripple and overall torque for Case I in detail for complete range of TSR from 1.5 till 4.5 with an increment of 0.5. Similar trends are observed for other cases due to which torque ripple is plotted for remaining the Cases in Fig. 9. 4.1. Case I We plot the torque ripple and the overall torque magnitudes in Fig. 8 for TSR 1.5, 3.0, and 4.5. For the torque ripple, we observe two peaks for a complete revolution of a turbine blade. Sharp peak is produced in the torque ripple as the blade traverses the upwind region near q ¼ 90 when the relative angle of attack is maximum while a smaller peak is produced as the blade is around q ¼ 270 . The secondary peak is attributed to the wake generated by the blade during the upwind path reducing the relative velocity as the blade traverses the downwind path. In other words, the blade
Fig. 6. Grid independence study for (a) Case I and (b) Case IV.
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4.2. Case II The torque ripples at all the TSR values are combined together in a single plot as shown in Fig. 9(b). The overall trend remains the same. This is also expected because Case II is mere extension of 2D blade to form the unit span length of the wing with symmetric boundary conditions at the end. The maximum values of both positive and negative torques are generated for higher TSR values with the high positive torques on the upwind side and less negative values during the downwind path of the rotation. 4.3. Case III Tip effects are the very critical phenomenon which is usually shed from the airfoils type blades. Air from the bottom with high pressure tends to reach the lower pressure air on the top of the wing surface, this air movement is considered to be span wise flow that means it is spreading over the wing and the only point to reach the low pressure air region is flowing over the wing tip. In order to see the tip effects from the blades the domain is extended in the z direction (See Fig. 2(c)). Thus, the rotor region is completely surrounded by the outer domain. The domain is extended adequately so the boundary does not have any effect on the flow physics of the blades. The results are formulated over the range of tip speeds in Fig. 9(c). Due to the addition of tip effects, strong wing tip vortices are generated which reduce the aerodynamic lift and cause a substantial increase in the drag force which degrades the power output of the turbine. 4.4. Case IV
Fig. 7. Instantaneous vorticity contours plotted for three-dimensional configurations of the turbine.
shed by a turbine blade, around q ¼ 90 , convect through the wake and interact with the same blade when it reaches q ¼ 270 . It is established by comparing the time scales of vortex convecting through a distance equal to the diameter of the turbine with approximately 12 m/s, i.e. 2.5/12 ¼ 0.208 s. At TSR ¼ 1.5, angular velocity can be computed from Equation (1) as 14.4 rad/sec which corresponds to approximately 825 /sec (or 2.29 revolutions/sec). Thus, half revolution (q ¼ 90 to 270 ) would take around 0.218 s for a blade to traverse this distance. In order to make a comparative analysis of the performance of a turbine at different rpm (TSR), we plot cumulative torque over the range of rpm in the right column of Fig. 8. It depicts the performance gains and drops of the turbine with the changing rotational speeds. In general, the torque increases with the increase in TSR. We observe maximum magnitude of torque ripple for TSR ¼ 4.5. However, we also observe negative torque for the same TSR magnitude. It can be attributed to high rotational speed and, with sliding mesh method, are non physical. The torque ripple for all TSR cases are superimposed in Fig. 9(a) and compared with other cases.
The addition of the support arms, central shaft and hub results in low torque generation over the cycle for a TSR value as shown in Fig. 9(d). It appeared that it produced negative overall torques at high TSR values. In comparison to Case II (without central assembly), the torque ripple curve experience more negative torque while the blades are moving through the downwind path specifically between q ¼ 220 to q ¼ 360 . It is because of the effect of span wise flow, blade-tips and additional profile drag due to support arms and central hub assembly. Also, the effect is contributed to the extra drag and strong vortices generation with the addition of the extra assembly. The contours of vorticity magnitude further the explanation of the negative torques as a sudden rise in turbulent intensities, extra profile drags and increased vorticity has been observed with the addition of support arms and hub. 4.5. Case V A number of significant differences are observed for the complete turbine model case in comparison to the 2D case. Although, torque generation between the two cases is qualitatively similar, the average torque of 3D experienced a drop of 32% in comparison to that of 2D case. The simulated torque ripples at different TSR values are superimposed in Fig. 9(e) to determine the effect on the changing rpm on the performance. More momentous difference is observed in the downwind path than in the upwind. Positive torques are only produced between 210
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Fig. 8. Torque ripple (left column) and overall torque (right column) for Case I.
energy from the wind. It causes a substantial rise in both resistive loads and the drag friction. Thus, negative performance coefficients are observed for the turbines at high TSR (numerically). Practically, the turbine will slow down under the influence of the resistive loads.
It is interesting to observe that the magnitude of torque ripple in the upward region peaks around the same location whereas the location varies in downward side. It is mainly due to the flow disturbance generated in the wake of the blade varies for each Case. This disturbance convects and affects the torque ripple in the downward side.
5. Parametric quantification of geometric approximations 5.2. Overall torque In this section, we compare the performance parameters for all the Cases and quantify the effects of geometric approximations of a given VAWT design. We can thus identify the contribution of each component in the overall performance. Another aspect of these analyses is to optimize the VAWT design by performing numerical simulations through approximate design which can fairly depict complete turbine design. 5.1. Torque ripple We plot one complete cycle of torque ripple for all Cases at the TSR of 3 in Fig. 10. It is evident from the plots that the torque ripple follows a similar overall trend; however, its magnitude varies according to the case. As expected, Case I over predicts the torque ripple values as compared to all the 3D Cases IIeV. The addition of third dimension and support structure cause flow obstructions and vortices which degrades the torque ripple. The drop is more during the downwind side as compared to upwind.
The next parameter evaluated from the numerical results is the overall torque for all the Cases. Since the overall torque is the combined effect of all the blades, it is strongly affected by individual torque ripples. The overall torque at the TSR of 3 is plotted in the Fig.11. Again, Case I results in the maximum value. The addition of third dimension and support structure affect spanwise flow, tip vortices and cause additional profile drag which reduce the overall torque. Thus, the overall torque decreases as we move from Case I to Case V. We also note that the overall torque goes negative for Case V. It means that a complete 3D VAWT will cease to operate contribute positively when the rotational crosses a certain thresh hold value. It is because the rotor blades will be rotating so fast that a possible stagnant localized zone will be generated in the rotor region. It will decelerate the rotating blades and extracted energy will go down to zero. However, since in CFD solution, a TSR value is forced. Hence, it is not possible to capture this dynamics and instead a negative performance coefficient is depicted.
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(a)
(b)
Fig. 10. One torque ripple cycle for different cases.
5.3. Performance coefficient
(c)
(d)
The performance coefficient shows a decrease in performance from Case I to Case V. The results are plotted in Fig. 12. The maximum value for Case I is around 0.5. For all the cases the performance coefficient curves starts with a lower value reaches a maximum value (at TSR ¼ 3) and drops to lower values. One important observation is the sudden drop in performance of the turbine with support structure at high rpm. This is because of the whirlpool effect the turbine experience at high rpm. The blade starts to rotate so fast that they do not properly interact with on coming air resulting in a substantial decrease in the performance. As we have forced the rotation to the rotor region, thus this effect is only numerical. It is also interesting to note that performance coefficients in Case II and III follow each other very closely. In other words, the tip effects are minimal in computing the overall turbine power. Similarly, Cases IV and V indicate that the effect of structural components is dominant as compared to the tip effects. Inclusion of support arm, central hub and shaft decreases the overall performance coefficient. The results for all five cases are also quantified in Table 2. As indicated earlier that Case I over predicted the torque values. To quantify the decrease in the performance, we compute the relative difference and term it “geometric” error due to structural approximations. In physical sense, it is the over prediction of twodimensional simulations lacking third dimensional flow. Fig. 13 plots the percentage drop in the performance for the Cases relative to Case I. We find that a percentage drop in performance of 18%
(e)
Fig. 9. Comparison of torque ripple for (a) Case I, (b) Case II, (c) Case III, (d) Case IV and (e) Case V.
Fig. 11. Overall torque for one complete rotation.
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Fig. 13. Percentage drop in power relative to Case I (2D).
Fig. 12. Power coefficient for different cases.
is expected from simple 2D (Case I) to simple 3D (Case II) simulations. By addition of tip effects from the blades (Case III) an additional 3% drop is observed. Further incorporating the three dimensional support structures (Case IV) the overall drop jumps to 26% relative to the 2D analysis. With the addition of tip effects in the support structure (Case V) the drop reaches to 32%. Usually researchers exclude the support structure (support arms and central hub) to focus on VAWT blades only, thus they should expect approximated error of 10%e12%. Practically, the results of Case V are expected to be in close agreement with the real-time results as they have the highest level of complexity with lower approximations. 6. Conclusion A detailed insight of the flow physics of VAWT is presented. Torque ripple at different conditions is explained. It can be concluded that it is very important to quantify and understand the effect of various levels of approximations done in CFD simulations. This finding high lights the fact that care must be taken in drawing conclusions based on pure 2D simulations, or simulations with no tip effects for performance of any VAWT. This study gives an overview of possible error in predictions due to various approximations. The optimum performance of a VAWT depends on its rotational speed. In present study, it is found at a TSR value of 3. A simulation done in 2D can over predict the performance up to 32 percent in comparison with real time 3D CFD simulation. The support structure of the under consideration VAWT consists of the supporting arms, central hub and the shaft. If we neglect the support structure in 3D simulations (only blades), then the tip effects can cause a difference of upto 3% in performance coefficient prediction. However, if the support structure is considered in the 3D simulations, the tip effects can cause upto 6%. The difference of results from 3D (blades only) and complete 3D with support structure; both with the tip effects is computed as
Table 2 Cp vs TSR for all Cases. TSR
Case I
Case II
Case III
Case IV
Case V
1.5 2 2.5 3 3.5 4 4.5
0.191 0.29 0.423 0.51 0.458 0.347 0.122
0.159 0.265 0.353 0.415 0.381 0.289 0.102
0.165 0.265 0.353 0.415 0.381 0.289 0.102
0.145 0.245 0.324 0.343 0.305 0.191 0.091
0.161 0.261 0.342 0.361 0.311 0.201 0.073
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