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Energy 175 (2019) 278e291 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Steady wind performance of a 5 kW three-bladed H-rotor Darrieus Vertical Axis Wind Turbine (VAWT) with cambered tubercle leading edge (TLE) blades ~ o a, Louis Angelo M. Danao a, b, * Ian Carlo M. Lositan a b Energy Engineering Graduate Program, University of the Philippines Diliman, Quezon City, 1101, Philippines Department of Mechanical Engineering, University of the Philippines Diliman, Quezon City, 1101, Philippines a r t i c l e i n f o a b s t r a c t Article history: Received 9 November 2018 Received in revised form 18 February 2019 Accepted 6 March 2019 Available online 11 March 2019 The performance of a 5 kW three-bladed H-rotor Darrieus Vertical Axis Wind Turbine with cambered Tubercle Leading Edge NACA 0025 blades was established using computational ﬂuid dynamics. 3D models and simulations of the VAWT were realized using CAD and CAE software, after which postprocessing analyses provided understanding of the VAWT and blade ﬂow physics. Results showed the TLE to be detrimental to ﬂow and performance of a cambered VAWT. Using torque, lift and drag data, the cambered TLE VAWT was shown to deviate signiﬁcantly against the cambered VAWT over one complete converged rotation. Cambered TLE VAWT blades encounter reduced lift forces and increased drag forces leading to lowered and eventual reversal of torque values. The z-vorticity and Q-criterion visualizations further supported the numerical results with the post-processed images showing vortices the size of the blade chord generated at blade wakes of the cambered TLE. The vortices emanate from the ﬂow separation at the blade crests creeping in at the blade trailing edge at 75 azimuth and reaching halfway through the blade chord length at 106 azimuth. Spanwise separation was observed to be restricted at blade crests. The resulting ﬂow degradation translated to the poor performance of the wind turbine. © 2019 Elsevier Ltd. All rights reserved. Keywords: TLE Camber VAWT CFD 1. Introduction Wind turbine performance, and therefore power generation, rely heavily on aerodynamics. Airfoils aerodynamically designed for aircraft have only been adopted as wind turbine blades [1]. Disregarding structural considerations, which presents additional design variables, blade design alone greatly impacts turbine ﬂow behavior across a wind stream. Force-velocity analyses of a vertical axis wind turbine (VAWT) blade across a wind ﬂow as shown in Fig. 1 generally depicts VAWT performance to be improved by increasing the lift force FL, decreasing the drag force FD while optimizing the angle of attack (AOA) a. The turbine blade rotating at a speed u about an axis of radius R has blade velocity Vb, the product of u and R, summing up vectorially to a resultant velocity Vr with the local wind velocity V, which emanates from the freestream wind velocity U. The blade tangential and normal forces FT and FN, * Corresponding author. Energy Engineering Graduate Program, University of the Philippines Diliman, Quezon City, 1101, Philippines. E-mail address: [email protected] (L.A.M. Danao). https://doi.org/10.1016/j.energy.2019.03.033 0360-5442/© 2019 Elsevier Ltd. All rights reserved. respectively, decompose into the forces FL and FD via the resultant force FR. Overall turbine conﬁguration is likewise a factor to turbine performance. For the case of rotor solidity, higher solidity VAWTs or those with three blades perform better than two-bladed counterparts over most of the operating range [2]. The use of motion controls to further improve wind turbine performance is also a practice. Leading edge slats and ﬂaps are widely used active controls in airfoils effectively increasing cambering and improving the ﬂight or ﬂow of the airfoil by improving lift characteristics [3]. Motion control can also be passive, meaning built-in stationary modiﬁcations or immovable parts attached to a body surface inﬂuencing ﬂow dynamics. Cambering and tubercle leading edge (TLE) are two such passive motion controls [4]. Cambering in airfoils is the modiﬁcation of its crosssectional symmetry. Whereas a symmetrical airfoil has its top and bottom cross-sectional proﬁle symmetrical with respect to an axial or horizontal plane cutting across its centroid, a cambered airfoil introduces convexity to the proﬁle, so the top and bottom halves of the airfoil are asymmetric. The TLE, oftentimes referred to as leading edge serrations, are undulations on the leading edge formed by the wavelike impression of the protraction and ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan retraction of the airfoil proﬁle from end to end of the blade length. TLE is a biomimetic structure based on the tubercles on humpback whale (Megaptera novaeangliae) ﬂippers [5]. Cambering has been shown to enhance lift [4,6], improve lift-todrag ratios, delay stall [6], and increase rotor performance [4,6e8] by increasing torque and thrust values [6,8] of H-rotor Darrieus VAWTs. Meanwhile, TLE effects vary with VAWT design and operational conditions. Wang and Zhuang [9] effectively applied TLE in a low tip speed ratio (TSR) setting two-bladed H-rotor Darrieus VAWT, conducting a parametric computational ﬂuid dynamics (CFD) study on TLE dimensions of wavelength and amplitude, and Reynolds number. TLE was shown to generally improve the baseline VAWT design at lower TSRs, favoring lower wind speeds. At 3 m/s, 0.061 or a 50.1% increase in coefﬁcient of performance (CP) was noted in the TLE VAWT against the baseline, with increases lowering non-linearly as wind speeds increase. Flow physics further revealed the suppression of ﬂow separation and increased torque in the TLE VAWT due to counter-rotating vortex pairs in the TLE serrations. Conversely, the results of Bai et al. [10] for a low TSR three-bladed H-rotor Darrieus VAWT present the TLE to be detrimental to performance in that the thrusts of the VAWT blades with TLE decreased signiﬁcantly. The combined effects of both cambering and TLE have only been documented in standalone airfoils [11]. TLE and cambering advances post-stall recovery and enhances lift to improve airfoil aerodynamic performance. Separately, each have been shown extensively to better airfoil performance. To improve the lift at a certain angle of attack, a greater camber is advised [3]. The effective use of camber improves the lift coefﬁcient of airfoils, be they the systematic, serial NACA family of airfoils or any other airfoil [12]. In airfoils, TLE increases lift and stall angle, reduces drag to delay separation, and minimizes tip stall to restrict spanwise ﬂow [4]. Hansen [3], along with Wang and Zhuang [9] and Bai et al. [10] for VAWTs, concluded that keeping the TLE amplitude-to-wavelength ratio, A/W, low resulted to the best airfoil and VAWT performances, respectively. In other studies, TLE in airfoils were shown to increase the maximum lift by 4.8%, lift-to-drag ratio by 17.6%, and decrease induced drag by 10.9% [13], and observed to positively inﬂuence laminar separation or bubble formation near the leading edge, dynamic stall and tonal noise [14]. 279 Fig. 1. Force-velocity analyses of turbine blade across a wind ﬂow. With limited available research on VAWTs and particularly the inﬂuence of TLE to its performance, this CFD study investigated the steady wind performance of a 5 kW three-bladed H-rotor Darrieus VAWT with TLE and cambering as passive motion controls on the NACA 0025 blades. VAWT research stalled in the 1990s in favor of the more commercially viable horizontal axis wind turbine (HAWT) and is only currently gaining momentum. The United States is into offshore VAWT research having exempliﬁed large scale Darrieus VAWTs to perform well against similar capacity HAWT equivalents [15]. Using models like the two-equation eddy-viscosity k-u shear stress transport (SST) turbulence model, CFD applies time- or Reynolds-averaging to numerically solve the mass conservation and momentum equations in three dimensions e the Navier-Stokes equations e as a function or not of time. This study used the k-u SST turbulence model because it provides detailed and accurate information in near-wall regions while allowing freestream independence in the farﬁeld [16]. It has been shown to ably predict airfoil experimental behavior [17], and correctly duplicate VAWT experimental results with 2D and 3D models [2,18]. Besides appropriateness of turbulence model, its agreement with the CFD VAWT model is needed, to which mesh studies are pursued for validation and optimization. To match VAWT model meshes to the corresponding turbulence models, yþ is used as blade near-mesh quality indicator [18]. With their mesh convergence study, Zadeh et al. [19] correlated mesh quality with convergence: Nomenclature FL FD a u R Vb Vr V U FT FN FR CP A/W yþ c z A W lift force drag force angle of attack rotational velocity rotor radius blade velocity resultant velocity wind velocity freestream wind velocity tangential force normal force resultant force coefﬁcient of performance amplitude to wavelength ratio dimensionless wall distance blade chord length blade length along the z-direction amplitude wavelength N N rad/s M m/s m/s m/s m/s N N N dimensionless dimensionless e M M M m L Ds u* y v Re l Dt q N TB r A Cm Cl Cd CL CD PW characteristic length ﬁrst cell height friction velocity at the nearest wall distance to the nearest wall kinematic viscosity Reynolds number tip speed ratio time step azimuth angle number of blades net blade torque density area coefﬁcient of moment lift coefﬁcient drag coefﬁcient corrected lift coefﬁcient corrected drag coefﬁcient wind power m m m/s m m2/s dimensionless dimensionless s e Nm kg/m3 m2 dimensionless dimensionless dimensionless dimensionless dimensionless W 280 ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan the ﬁner the mesh, the more accurate the solutions and reﬁned the ﬂow visualizations were. 2. Methodology 2.1. Study framework Computer-aided design (CAD) and computer-aided engineering (CAE) software were used to make the VAWT models, run transient numerical simulations on the models to quantify wind ﬂow parameters needed to compute CP values and other derived quantities, conduct further analyses such as lift and drag characterization, and post-processing for the comparative performance analyses between the baseline NACA 1425 (cambered) airfoil VAWT and that with TLE (cambered TLE). CFD requires proper discretization e geometry modeling of the design VAWTs and meshing of the ﬂuid environment e of the domain, solver settings and calculation, and post-processing. The VAWT geometry and domain boundaries were constructed to their actual sizes for use in meshing the ﬂuid environment. The need to properly discretize the mesh and set its boundary conditions required model validation against baseline experimental and CFD results of performance curves of similar 5 kW capacity threebladed H-rotor Darrieus NACA XX25 VAWTs from literature [6,20] in lieu of actual experimental validation. Both the baseline results have discretized 2D domains. Thus, a transitional 2D model was ﬁrst constructed and validated prior the actual CFD studies in 3D. Starting off with the 2D model, parametric studies on the yþ, blade node density and time step were performed to optimize simulation settings. The yþ study resolved the boundary layer requirements of near-wall cells, particularly the cell meshes surrounding and nearby blade surfaces. The node density study determined a suitable if not optimal cell size distribution near the critical areas of ﬂow, which are the cells near and adjacent to the leading and trailing edges of the blades. The time step study optimized the temporal distribution of the wind ﬂow across the VAWT. It is necessary to set the appropriate node density and time step in the simulations to fully capture the wind ﬂow regime across the blades without missing out on key ﬂow phenomena while computationally ofﬂoading the solver. Performance analyses involved examining the torque results and determining the CP of the two VAWT models, lift and drag characterization of the ﬂow, and ﬂow visualizations. These gave detailed insights into the ﬂow behavior of the VAWT with its cambered TLE blades. Solver ANSYS® Fluent® 18 was used for all simulations. A 64-bit desktop computer with four physical cores, eight threads operating up to 3.4 GHz frequency, and with 16 Gb DDR4 RAM was used for the study. Fig. 2. (a) Isometric and (bed) orthographic views of the cambered TLE blade geometry. extruded along the z and ez directions by 0.3 m each so the full test wing span measured 0.6 m. Each 3D cambered blade was treated as an inﬁnitesimally small portion of a continuously long blade since the geometry ends were to be set as symmetric boundary conditions in the mesh. To come up with the TLE surface on the leading edge, the airfoil proﬁle was lofted along the path of the sinusoidal wave given by (1) situated along the 0.6 m length span in the z-axis such that the chord ends on the leading edges of the lofted airfoil proﬁle coincided with the wave. Equation (1) is a generally accepted deﬁnition of TLE in NACA and VAWT airfoils [3,10]. LðzÞ ¼ A cosð2pz=WÞ (1) TLE amplitude was set to 0.02 m and wavelength 0.2 m to keep the A/W ratio low at 0.1 or the amplitude at 10% of the wavelength. The wavelength is 4/3 of the chord. The 3D cambered TLE geometry was likewise treated as an inﬁnitesimal blade unit with both of its ends terminating in the sinusoidal wave crests. Fig. 2 shows the isometric and orthographic views of the 3D cambered TLE model where the resulting modiﬁed blade has three tubercles on the airfoil leading edge. Fig. 3 shows a comparative perspective of the 3D (a) cambered and (c) cambered TLE blades where Fig. 3b shows the former containing the latter to highlight their geometric differences. The computational domain was discretized into the rotor and stationary farﬁeld sub-grids compliant with the sliding mesh technique. The rotor sub-grid is a 4.2m-diameter cylinder containing the VAWT geometry with the center hub centered at the origin of the x-y-z Cartesian coordinate system. This was so as a signiﬁcant extension of the ﬂuid around the VAWT rotates with it in fully developed ﬂows. The rotor sub-grid is contained in a cylindrical opening in the farﬁeld sub-grid, which is dimensioned 30 m in width and 40 m in length, with the shorter sides to the left and 2.2. VAWT CFD model The wind turbine designed is a 3.0m-diameter three-bladed Hrotor Darrieus VAWT with airfoil blades having chord lengths of c ¼ 0.15 m. The baseline cambered airfoil used is NACA 1425 or NACA 0025 with 1.5% camber. Assumed aerodynamic center of the airfoil is 0.0375 m from its leading edge along the airfoil chord line. Pitch angle was set to zero with no provision for pitching throughout the azimuthal rotation. The geometry foregoes struts and other blade support structures for faster numerical computations by neglecting drag and blockage effects. Only the center hub or post, about which the blades rotate, remain in the geometry as it poses wake effects to a blade downwind. To generate the three-dimensional (3D) cambered geometry, the two-dimensional (2D) airfoil shape resting on the x-y plane was Fig. 3. Perspective views of the (a) cambered TLE blade, (b) overlain blades and (c) straight cambered blade. ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan right of the rotor, and the lengths up and below equidistant to the rotor. The farﬁeld sub-grid extends up, below and left of the rotor 15 m or ﬁve rotor diameters away from the center hub, and to the right, 25 m away. This conﬁguration allowed for the treatment of the wind ﬂow across the rotor as an unobstructed stream emerging from the leftmost end of the farﬁeld and exiting its farthest right. For the 3D geometry, both the rotor and farﬁeld sub-grids are 0.2 rotor diameter or 0.6 m thick. Fig. 4 shows the dimensioned 2D geometry. The rotor and farﬁeld sub-grid domains each necessitated a unique discretization and thus were meshed separately and differently. The farﬁeld domain is coarse and fully unstructured with its domain ends divided into nodes of 1 m spacing while the circular hole housing the rotor sub-grid is dimensioned to be less than the blade chord c ¼ 0.15 m or around 0.11 m. All unstructured mesh cells were generated automatically with the Advancing Front Ortho algorithm and anisotropic tetrahedral extrusion inherent to the meshing software. The 2D farﬁeld mesh was generated growing cells from the circular hole to the domain ends. While fully unstructured, its mesh remained quadrilateral-dominant (quaddominant) with a boundary decay of 0.95 and cell growth of 1.1. Having a quad-dominant 2D farﬁeld mesh translates to an equivalent 3D mesh largely populated by tetrahedral cells (tets). The 3D mesh remained a hybrid mesh of tets, prisms, pyramids and hexahedral cells (hexes). The objective of creating quad-dominant and, consequently, tetrahedral-dominant (tet-dominant) meshes is reducing the cell population since two or more triangular cells usually make up a quadrilateral (quad) and reducing the cell population saves on computational time. The 3D farﬁeld volume mesh also has a cell growth of 1.1 and boundary decay of 0.95. This volume mesh grows out from the 3D domain interior to the seven (7) surface mesh extents of the farﬁeld e the velocity inlet and pressure outlet surfaces to the left and right, respectively, of the rotor sub-grid; the wall surfaces up and below the rotor sub-grid; the two surfaces of symmetry adjacent and perpendicular to the two walls, and velocity inlet and pressure outlet surfaces; and the circular interface centered at (0, 0, 0) of the x-y-z Cartesian coordinate system. All surface nodes of the 3D surface planes were discretized according to the spacings speciﬁed for the 2D mesh. Comprised of inner structured and outer unstructured cells, the rotor sub-grid involved more detailed meshing. Starting with the 2D domain, three structured mesh control circles or O-grids were created before growing the cells from the bounds of these control circles to the extents of the rotor sub-grid as an unstructured mesh. ANSYS® requires a minimum of 10 structured cell layers normal to a wall to fully capture shear ﬂow layers [16]. This general Fig. 4. The dimensioned 2D model geometry. 281 requirement for wall boundary layer simulations holds true for the k-u SST turbulence model and the VAWT blades experiencing viscous shear forces were treated accordingly so. This was done by conducting a yþ study on the rotor sub-grid. The mechanism of creating O-grid structured meshes involves building layer upon layer of cells from the wall boundary until the preferred cell layer thickness, and the cell height of the ﬁrst cell layer adjacent to the blade, hereafter referred to as the ﬁrst cell height Ds, was identiﬁed with the yþ study. The O-grid cell layer thickness also varied depending on the expansion of the cells based on the yþ. The yþ deﬁned by (2) is a dimensionless parameter for wallbounded ﬂows that qualiﬁes the mesh ability to model the ﬂow. It is model-speciﬁc and for the k-u SST turbulence model, the acceptable yþ ranges are 0.1e1, 1 to 5 and 30 to 300 where higher values yield longer ﬁrst cell heights and, therefore, coarser meshes. yþ ¼ ðu*yÞ=v (2) þ A wide range of y values were used in the study. Particularly, representative yþ values of 0.1, 1 and 30, with the ﬁrst as baseline, were used to compute for the Ds values needed in meshing the control circles of the rotor sub-grid. The yþ study required checking yþ values of the ﬁrst cell layer cells after full steady wind simulation to see if values were within the or out of range. yþ values out of range mean unacceptable results, disqualifying the mesh. Meshing of the remaining portion of the rotor sub-grid and farﬁeld domains proceeded as previously detailed to come up with the 2D VAWT model prior further simulations. Establishing the correct yþ value resolves the viscous sublayers of all three VAWT blades, thus allowing for provisions to coarsen the mesh, which should save meshing and computational time. Cell growth and boundary decay from the control circles and post to the extents of the rotor sub-grid are 1.1 and 0.3, respectively. These settings ensured the cells grew out from the domain interior slower than those in the farﬁeld so more cells populated the domain and complied with the target cell size and skewness. Average cell size in the rotor sub-grid needed to be less than the chord length of c ¼ 0.15 m. For cell skewness, the acceptable average for the mesh is 0.6. Coming up with the 3D rotor sub-grid mesh involved initially creating surface meshes on the VAWT geometries e the blades and post e and then growing the volume mesh from these surface meshes to those at the extents of the rotor sub-grid. To fully resolve the boundary layer of each blade in the volume mesh, the same optimal yþ setting resulting from the 2D domain yþ parametric study was sought. To attain this yþ setting in 3D, the cells surrounding the blades up to 90 layers were fully structured hexes. Beyond the 90th hex-cell layer, cells grew out to the extents of the rotor sub-grid as a fully unstructured mesh of tets and pyramids. Cell growth and boundary decay in the entire rotor sub-grid followed that of the 2D domain. As to the rotor sub-grid dimensions, those of the 2D were maintained. Thus, the ﬂuid rotor sub-grid is cylindrical or an extrusion of the 2D circular domain to a depth of 0.6 m with its cylindrical center at (0, 0, 0) of the x-y-z Cartesian coordinate system. The optimal node density of the 2D blades were also imposed on the 3D blades. In total, 10 surface meshes were created for the rotor sub-grid. Each blade has one each for its upper and lower cambers. The post has one. The rest of the surfaces are for the cylindrical ends of the rotor sub-grid e the rotor interface sliding with the farﬁeld interface and the two symmetrical circular surfaces. These two symmetrical circular surfaces have their inside mesh terminate with the outlines of the post and three blades. The 3D domain is represented by Fig. 5 where the vertical dimension is blown-up 42 times that of the x and y axes to emphasize the rotor sub-grid ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan 282 Fig. 5. Dimensions and surface boundary conditions of the 3D domain. containing the blades. Also, during meshing, most importantly of the rotor sub-grid, careful consideration leaned towards the following mesh characteristics: cell size, cell skewness and cell population. As stated, the average cell size in the rotor domain was kept to less than c ¼ 0.15 m and cell skewness to z0.6. Cell population was kept in check as reaching six (6) million cells crashed the solver. Both cell size and cell skewness conditions promote convergence of results and therefore computational time advantages. Gravitational effects, having a negligible inﬂuence on the VAWT operation, was disregarded in the 3D VAWT model. 2.3. Steady wind simulation The steady wind simulations were transient, pressure-based. Rotor sub-grid rotation was set to a constant rotational velocity based on the TSR setting. With freestream wind velocity at the left end of the farﬁeld domain constant at U ¼ 5 m/s, the rotational velocity is Vr ¼ 13.33 m/s at the peak TSR l ¼ 4. The right end of the farﬁeld domain served as pressure outlet while the upper and lower bounds were set to stationary no-slip wall zones. To accomplish the sliding mesh setup, the rotor sub-grid boundary and the circular hole of the farﬁeld domain were interfaced with each other, both interfaces sliding past each other during rotor rotation to allow ﬂow continuity from the farﬁeld domain cells to and through the rotor sub-grid. For the 3D domain, the upper and lower depths with the blade ends were treated as symmetrical surfaces and set as symmetry zones. k-u SST turbulence model was used for the transient steady wind simulations and solve the pressure-based RANS equations. This model is ﬁt for the low Reynolds number values of the ﬂow under study averaged to be Re ¼ 4.96 104 at the peak TSR of l ¼ 4. Default settings of the k-u SST turbulence model were used, with the Production Limiter option toggled on for turbulence energy correction in the u equation. Gradient evaluation method was Least Squares Cell-Based. Pressure, momentum, turbulence kinetic energy and speciﬁc dissipation rate interpolating schemes as well as the transient component were all of second order. Pressure and velocity were also coupled. Benchmark validation of both the 2D and 3D models required the recreation of performance curves by simulating the VAWT over a TSR range. For the 2D model, TSR range was one (1) to six (6) taken at one (1) unit increments with half increments between the TSR values of three (3) and ﬁve (5). The 3D model TSR range was from 3.5 to ﬁve (5) at half increments. Each simulation required 10 complete rotor revolutions for the solution and residuals to converge. Residual convergence was set to 1 106. The 2D node density study resolved how dense and aggregated cells should be, more speciﬁcally those adjacent to the blade walls and those running through the leading and trailing edges. Node density spacing at the leading and trailing edges were set to 0.0002 m. Constraining the cells in the leading and trailing edges provides better resolution of the area, which are of high curvatures and angles. Adjustments to this node spacing were done accordingly in response to cell aspect ratio values. The following blade node densities were considered in the node density study: 100, 210 and 300. Node density of 210 was set as baseline. The 2D time step study involved the determination of the best ﬁtted time increment to model the actual ﬂuctuation of the ﬂuid ﬂow across the domain. To simplify the resolution of the transient model simulation with respect to the azimuth angle rotation, it was deemed best to assume a certain degree of rotation as equivalent to one (1) time step. Three azimuth angle rotations were considered: 2 , 1 and 0.5 . The equivalent time step Dt was computed using (3). Dt ¼ ð2pqÞ=ð360uÞ (3) To select the appropriate time step, the torque results of the fully converged simulation rotations of all azimuth angle options were compared. Azimuth angle q ¼ 1 was set as the baseline setting from which the two azimuth angles were compared to. 2.4. Performance analyses and post-processing To analyze the performance of the VAWT, it was necessary to plot the CP values at different TSRs. To compute the mean CP for one full rotation, the instantaneous coefﬁcient of performance (Cp) values for the last rotation were averaged. The instantaneous Cp for each torque value was determined using (4). CP values were then plotted against the TSR to come up with the performance curve and relate the performances of the VAWT models. Cp ¼ ð2N uTB Þ . rAV 3 (4) The net blade torque TB is the sum of the individual blade torques Tb at a time step instance. Individual blade torques were computed using (5) given the coefﬁcient of moment (Cm) values monitored individually for the blades throughout the simulation. The torque results plotted against the time step is the torque chart. Tb ¼ 0:5rV 2 ARCm (5) Lift and drag characterization, along with ﬂow visualizations from post-processing of the 3D results provided a parametric and visual understanding of the ﬂow physics of the VAWT. In this regard, the coefﬁcients of lift Cl and drag Cd were also monitored during the simulations. The monitored values were then corrected and transformed based on the geometric angle of attack and blade azimuthal position using Equations (6) and (7). Flow physics offer detailed representations of the ﬂuid vortices and ﬂow ﬁelds in relation to the numerical results of the study. . 0:6cV 2r (6) . CD ¼ ½Cd cosðq aÞ þ Cl sinðq aÞ 0:6cV 2r (7) CL ¼ ½Cd sinðq aÞ Cl cosðq aÞ 3. Results and discussion 3.1. 2D model validation The net blade torque measurements of the 2D model validation ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan 283 Fig. 6. TB values for the 10 rotations of the 2D baseline mesh. Fig. 8. Individual Tb for the last VAWT rotation. for convergence at the peak TSR l ¼ 4 with one time step set to q ¼ 1 are presented in Fig. 6. The torque chart showing all 10 rotations depict cyclical convergence visually noticeable at the beginning of the ﬁfth rotation. Fig. 7 supplements this with the overlain net torque curves per rotation for all 10 rotations showing indistinguishable differences of the curves from the seventh rotation onwards indicating cyclical convergence. On average, the cycle-averaged torque during the ninth rotation varies by 5.0% with that of the last rotation. Besides cyclical convergence, numerical convergence was also achieved with all conserved variables falling below the minimum of 1.0 106, indicating acceptability of the results and the CFD model. The coefﬁcient of performance is CP ¼ 0.32, which is well within the tolerated range for Darrieus VAWTs [21]. The value is 6% lower than the results of Bausas and Danao [5] for a similar setup but is still higher compared to the CP value for their symmetrical airfoil VAWT. The CP value obtained was averaged for the last VAWT rotation harnessing from the available wind power of WP ¼ 229.7 W. In Fig. 8, breakdown of the net blade torque into the individual blade torques of the three blades for the 10th or last rotation show the individual blade torques to be mostly positive throughout the converged range signifying the positive net performance earlier noted with the CP and TB values. Here and in succeeding charts with individual blade references, blade 1 denotes the VAWT blade initially at azimuth q ¼ 0 or upwind at the start of the rotation, blade 2 at azimuth q ¼ 120 and blade 3 at azimuth q ¼ 240 . The same individual blade torque values when overlain by adjusting the two lagging blades by 120 and 240 accordingly as shown in Fig. 9 show the cyclic nature of steady wind dynamics occurring in one rotation: all three blades experience the same phenomena at every azimuthal position. Besides convergence, the mesh needed checking of yþ values of blade-adjacent cells. Set to yþ ¼ 0.1 during meshing, monitored yþ values for the baseline mesh needed to be always within the acceptable range of 0e1. Fig. 10 is a scatterplot of the last yþ values of near-wall or blade-adjacent cells for all three blades where all 630 cells for all blades have yþ values within the required range. Throughout the last converged rotation, these cells had yþ values oscillating within the acceptable range, signifying the mesh to successfully model the k-u SST turbulence model and therefore the VAWT as well. The baseline 2D mesh shown in Fig. 11 has 54,000 cells in the mixed-cell rotor sub-grid and 8634 in the fully unstructured farﬁeld sub-grid. Maximum cell edge length in the rotor sub-grid is 0.13601856 m or 0.9c.cC, observed particularly in the unstructured Fig. 7. Overlain TB chart per rotation of 2D baseline mesh. Fig. 9. Overlain individual Tb over the last 0 e360 VAWT rotation. 284 ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan Fig. 10. Blade yþ values for the last instance of the baseline mesh. 3.1.1. Parametric studies Simulation runs for the yþ values of 1 and 30 yielded torque curves departing from the baseline yþ value of 0.1. The same simulation procedure of 10 complete VAWT rotations at the peak TSR and time step setting of one time step equivalent to q ¼ 1 was used. The torque curve of yþ ¼ 1 coincided with that of the baseline but remained asymptotic and underperforming throughout the rotation, varying even by 2.1Nm utmost against the baseline at some point upwind. On average, its torque differed against the baseline by 21.1%. Those of yþ value of 30 varied by 89.6% on average against the baseline. Furthermore, both test meshes have blade-adjacent cell yþ values at the last converged rotation outside the range limits. The mesh with yþ ¼ 30 has blade-adjacent cell yþ values below the minimum acceptable of yþ ¼ 30, and the yþ ¼ 1 has values exceeding the maximum of yþ ¼ 5 although numbering only a few cells in the upwind leeward portion of the ﬂow. As a result of this yþ study, the baseline mesh was deemed appropriate for the VAWT model of the study. 3.1.1.1. Node density study. The node density study resulted with the baseline and 300-node density meshes having torque curves overlapping e differing by 0.92% on average e throughout the converged duration of the last two VAWT rotations. Meanwhile, the 100-node density mesh underperformed cyclically compared to the two, with a mean difference of 6.29% against the baseline. Given the similarity of results of the baseline and 300-node density meshes meant the lower density baseline mesh behaved much the same way with the other, and therefore was adequate to stand in for the higher density 300-node density mesh. 3.1.1.2. Time step study. For the time step study, the baseline mesh was run full 10 VAWT rotations using the time step settings of 0.5 and 2 . Using (3), Dt and no. of time steps were 0.000654498s and 1,800, respectively, for q ¼ 0.5 , and 0.002617994s and 7,200, respectively, for q ¼ 2 . The resulting torque curves showed the baseline time step and time step setting of q ¼ 0.5 to vary only by 0.0871% suggesting their similarity and therefore interchangeability. Increasing the time step to q ¼ 2 , on the other hand, yielded an offset torque curve intersecting the baseline every 120 and differing against it by 12.0% on average, which clearly depicted deviation between the two. The baseline time step setting, therefore, was useable in place of the lower time step for having similar converged results in half the computational time. The former runs twice faster than the latter since at the peak TSR, the baseline mesh required 3600 time steps and the latter twice this for the same simulated time duration. Fig. 11. Baseline 2D mesh showing the rotor and farﬁeld sub-grids, and an O-grid around an airfoil. mesh outside the O-grid meshes around the blades. Inside the Ogrids grown to 90 cell layers at 1.1 cell growth, cell dimensions are in millimeter scales considering the blades have 210 nodes around each that are spaced 0.0002 m at the trailing and leading edges, and the ﬁrst cell height Ds ¼ 5.5,602,360,537 106. Maximum cell skewness is 0.81149165 at the rotor sub-grid but the averages are 0.22091140 and 0.04304509 for the farﬁeld and rotor sub-grids, respectively. Also presented are zoom-ins of the rotor sub-grid and an O-grid where the mesh structure is shown for appreciation of the cell layers, cell growth and other cell properties. 3.1.2. 2D model performance curve validation Using the baseline mesh as the optimal 2D VAWT model, simulation runs were performed for the speciﬁed TSR settings of the VAWT to arrive at the CP values over the identiﬁed operating range. Comparing the resulting performance curve of the 2D model validated its adaptability towards transitioning to the 3D model. The 2D model performance curve for the TSR test range of l ¼ 1 to l ¼ 6 is shown in Fig. 12 along with the reference performance curves where visual comparison of that of the 2D model against the reference curves show its general agreement to all. While the same trend can be observed for these performance curves, the output performance curve of the 2D model speciﬁcally conforms to the CFD results of Bausas and Danao [5] throughout the TSR range tested. Outside the peak TSR, VAWT performance similarly drops profoundly to zero at TSR values l ¼ 2 and l ¼ 6. The 2D model was then apt for adoption into the 3D model serving as basis for the meshing and simulation procedures. ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan 285 Fig. 12. Performance curve results. 3.2. 3D model validation With the aim of reducing cell count in the 3D model against the 2D, adjustment to its discretization was done accordingly. Nearwall cells around the blades needed compliance to yþ settings while mesh away from the blades towards the farﬁeld allowed for compromise. From 2D to 3D, the average cell size inside the rotor sub-grid was preserved at less than c ¼ 0.15 m. Cell skewness in all sub-domains was set to 0.6 like that of the 2D model. The farﬁeld sub-grid mesh, set with a boundary decay of 0.95 and cell growth of 1.1, is coarse and fully unstructured but still tet-dominant. The rotor sub-grid mesh is mixed-cell in nature. Meshes around the blades up to 90 cell layers are structured O-type meshes with Ds set to yþ ¼ 0.1, after which the meshes grow outwards unstructured with boundary decay of 0.3 and cell growth of 1.1. A cut-up along the x-y plane of the 3D mesh in Fig. 13 shows the cross-sectional cell distribution in that plane. This is a cross-sectional plane midway of the volumetric 3D mesh comparable to the planar 2D mesh in Fig. 11. Fig. 14a moreover shows a perspective view of the same crosssection zoomed-in on the blade and nearby cell structures. Table 1 details parametric details of the 2D and 3D meshes for additional feature-for-feature contrast and comparison. While the maximum skewness of the 3D cambered mesh reached 0.90178168 at a setting of 0.6, this value for some cells of the farﬁeld sub-grid is insigniﬁcant to the performance results as will be attested to by the succeeding mesh validation. The average of the parameter at 0.54546740 is also acceptable. 3.2.1. 3D mesh validation Before model validation, the resulting 3D cambered VAWT mesh needed mesh validation by comparing blade torque results against those of the 2D model. Computed individual blade torque results of the simulation at the peak TSR l ¼ 4 for 10 complete VAWT rotations were shown to converge cyclically. 3D cambered VAWT torque results were lower than that of the 2D model by a factor of 2/3 due to the geometric height of the 3D model at L ¼ 0.6 m. The 2D model blade depth is taken as unity. yþ monitoring on blade-adjacent cells have shown that the mesh sufﬁciently models ﬂuid ﬂow across the VAWT using the k-u SST turbulence model. All 4000 hex cells around the three blades in the last converged rotation have yþ values below 0.6. 3.2.2. 3D model performance curve validation At the peak TSR l ¼ 4, the performance coefﬁcient was computed to be CP ¼ 0.30. This value is lower than the 2D model result, which is expected given the more realistic ﬂow in three dimensions of the 3D model compared to the 2D. Together with the CP results from the simulations at the three other TSR values of 3.5, Fig. 13. 3D mesh of the cambered airfoil VAWT showing the rotor and farﬁeld subgrids, and a zoom-in of the O-grid around an airfoil. 4.5 and 5, the performance curve was plotted as shown in Fig. 12. While performance deviation also occurs at l ¼ 4.5, values at l ¼ 3.5 and l ¼ 5 were like that of the 2D. Overall, the results are acceptable given the observable similar trend in the performance curves of both models. 3.3. Performance analyses of the cambered TLE VAWT Meshing of the 3D cambered TLE VAWT mesh was procedurally the same with that of the 3D cambered mesh. To generate a 3D mesh control circle, a set of O-grid planar meshes along the blade depth in the z dimension were extruded continuously from trough to crest, crest to trough, and alternately thereafter until the full blade length was covered. While procedurally the same with the 3D cambered mesh, this differed in the creation of ﬁve additional intermediary O-grid meshes to incorporate the TLE surface. The 3D cambered mesh has a straight leading edge requiring only one Ogrid extruded along the blade depth. Each 3D mesh control circle of the 3D cambered TLE VAWT mesh contains 540,000 cells or 180,000 more cells than the 3D cambered VAWT mesh. Control circle cells are all structured hex cells, particularly made so in consideration of the yþ requirements of the k-u SST turbulence model. The perspective view of a control circle in Fig. 14b gives a visual comparison of the cambered TLE blade against the cambered blade. Table 2 summarizes the parametric differences of the two 3D meshes. 3.3.1. Cambered versus cambered TLE VAWT performance The output torque curve for one blade of the cambered TLE ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan 286 The cycle-averaged torque of the cambered TLE blade in Fig. 15 is Tb ¼ 0.24Nm, which is a quarter of the torque generated with the cambered blade. This value also amounts to a net blade torque of TB ¼ 0.70Nm. Given an available wind power of PW ¼ 137.8 W, the TLE modiﬁcation reduced by 78% to 9.28 W the cambered VAWT power output of 41.63 W at the peak TSR l ¼ 4 over one full rotation. Simulations on the cambered TLE model at the other three TSR values of l ¼ 3.5, l ¼ 4.5 and l ¼ 5 depict the same trend in degraded performance as shown in Fig. 12. While the performance curve shifted its peak to the right, at the higher TSR value of l ¼ 5, the cycle-averaged torques for all TSR test values do not amount to more than the cycle-averaged blade torque of Tb ¼ 0.26Nm and the corresponding net blade torque of TB ¼ 0.79Nm at this new peak TSR. Detrimental effects of the TLE modiﬁcation on the performance of the 3D cambered VAWT remained remarkably profound throughout the TSR test range. Fig. 14. Zoom-in perspective views of the (a) cambered and (b) cambered TLE blades showing the structured O-grid volume mesh adjacent and surrounding each blade, and the surrounding unstructured meshes beyond their control circles. VAWT simulation is shown in Fig. 15 with that of the equivalent or coincident blade of the cambered VAWT. This is for a complete 360 rotation; the tenth or last converged rotation. Statistical convergence of results was noted with all equation residuals below the minimum of 1.0 106. Cyclical convergence of results was also achieved checking the superimposed individual blade torques and comparing the last two (2) rotations. yþ values of the 6000 walladjacent cells have also been monitored to be below 0.5, well within the required range of 0e1, thereby demonstrating successful modeling of the cambered TLE VAWT with the k-u SST turbulence model. 3.3.2. Torque analyses Differences in the performances of the cambered and cambered TLE VAWTs is visually straightforward in Fig. 15. Both blades follow the same torque curve path from the start at 1 but depart from each other at the azimuth angle of q ¼ 55 , therein labeled 2. From 2, the cambered blade remains trailing linearly towards its peak blade torque of Tb ¼ 4.57Nm at the azimuth of q ¼ 90 while the TLE blade had an earlier onset of torque reversal at the azimuth of q ¼ 74 , labeled 3. From 3, the torque of the cambered TLE blade dips until values become negative. This negative trend continues up to the lowest point of 3.59Nm, labeled 4 in the torque curve, at the azimuth angle q ¼ 106 . The observed progressive declining trend is linear and the shift in signs of the scalar torque values beginning at the azimuth angle of q ¼ 74 denotes blade motion reversal from counterclockwise to clockwise rotation. After the vertex of the torque curve at 4, moment reversal on the blade is comparably the reversed linear trend of the previous torque dipping, but instead of a full reversal, the curve experiences a setback in values in the azimuth angle range of q ¼ 132 and q ¼ 151. The torque just slightly recovers from then on and between the azimuth angles of q ¼ 180 and q ¼ 360 , labeled 5 to 1, torque values ﬂuctuate unlike the cambered blade although the average blade torque Tb over the range of both are the same at Tb ¼ 0.49Nm. 3.3.3. Lift and drag characterization Referring again to Fig. 15, during the period labeled 1 to 2 in the torque curve when both the cambered and cambered TLE blades have the same torque values, approximately the same lift and drag forces are experienced by both blades as shown labeled in the plots of CL and CD against AOA in Fig. 16 and Fig. 17, respectively. The same points of the torque curve of the cambered TLE blade in Fig. 15 are therein labeled accordingly in the plots of CL and CD. After point 2, Table 1 Parametric comparison of the 2D baseline and 3D cambered meshes. Average Skewness Maximum Skewness Maximum Edge Length Cell population Farﬁeld Rotor Farﬁeld Rotor Farﬁeld Rotor Rotor Farﬁeld Total Structured Unstructured BASELINE/2D MESH 3D CAMBERED MESH 0.22091140 0.04304509 0.68762318 0.81149165 1.3738530 0.13441569 54,000 5865 2769 62,634 0.54546740 0.15526986 0.90178168 0.83047406 1.4051636 0.21503057 1,080,000 586,420 21,253 1,687,673 ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan 287 Table 2 Parametric comparison of the 3D cambered and cambered TLE VAWT meshes. Average Skewness Maximum Skewness Maximum Edge Length Cell population Farﬁeld Rotor Farﬁeld Rotor Farﬁeld Rotor Rotor Structured Unstructured Farﬁeld Total Fig. 15. Individual blade torque curve comparison of cambered and TLE blades over one VAWT rotation at the peak TSR l ¼ 4. when the blade torque of the cambered TLE blade begins departing from the baseline, is when the lift coefﬁcient also begins decreasing and the drag coefﬁcient increasing. Arriving at point 3, the rate of change of drag coefﬁcient increases and more so after this. The lift coefﬁcient drops from its 0.80 peak at the azimuth angle of q ¼ 90 to 0.16, 11 after point 4. The cambered blade lift coefﬁcient peaks higher at 0.87 and 6 after that of the cambered TLE blade peak. From 3 up to the lowest point in the torque curve at 4, the cambered TLE blade encounters progressive linear decline in torque due to drag forces overturning the positive torque component on the Fig. 16. Lift coefﬁcient against the angle-of-attack plot at TSR l ¼ 4 for the 3D cambered and cambered TLE VAWTs. 3D CAMBERED MESH CAMBERED TLE MESH 0.54546740 0.15526986 0.90178168 0.83047406 1.4051636 0.21503057 1,080,000 586,420 21,253 1,687,673 0.54546740 0.15984145 0.90178168 0.86451892 1.4051636 0.24140802 1,620,000 554,642 21,253 2,195,895 Fig. 17. Drag coefﬁcient against the angle-of-attack plot at TSR l ¼ 4 for the 3D cambered and cambered TLE VAWTs. blade. The inversely increasing behavior of the drag coefﬁcient and torque peaks approximately at the maximum negative torque. The drag coefﬁcient curve of the cambered TLE blade is observed to peak 5 before the lowest blade torque at 4. Its lift coefﬁcient improves after 4 and continues decreasing to 14.47, past point 5 at the azimuth angle q ¼ 256 or 76 after 4. The cambered blade only drops slightly in lift coefﬁcient and, despite the same decreasing trend starting at the equivalent of point 4 of the cambered TLE blade, maintains a large gap in magnitude with the cambered TLE blade lift coefﬁcient up to point 5. Overall, from points 1 to 5, the only noted differences in the lift coefﬁcient of the two blades are the advanced peaking and lower peak value for the cambered TLE blade with the deviation beginning at point 2. Disparity in the torque reaction to notably abrupt lift and drag changes, such as the 6 earlier onset of torque reduction on the TLE blade against an increasing lift and decreasing drag, is attributable to hysteresis and blade force interactions. From these, it is imminent that lowering the lift and increasing drag reversed the net moments on both blades, with effects markedly intensiﬁed with the cambered TLE blade. After 5, lift coefﬁcient of the cambered TLE blade recovers with the torque so that between points 5 to 1 through Figs. 15e17, the averages for the blade torque, lift coefﬁcient and drag coefﬁcient are Tb ¼ 0.49Nm, CL ¼ 0.34 and CD ¼ 0.035, respectively. Except for its drag coefﬁcient averaged at 0.015, the cambered blade has the same average lift coefﬁcient with the cambered TLE blade over the same period as the torque. These make the azimuthal period between points 1 and 5 having marked signiﬁcant differences in torque, lift and drag of interest in the proceeding ﬂow visualizations. The Q-criterion and z-vorticity image renderings of the ﬂow visualizations detail the invisible wind dynamics of crucial 288 ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan moments of the ﬂow to support the torque, lift and drag observations herein presented. Figs. 16 and 17 also show the static airfoil plots of lift and drag coefﬁcients for a pitching NACA 1425 airfoil where the lift coefﬁcient plot shows the static airfoil to stall earlier than the VAWT blade equivalents but at a higher peak. Drag values of the static airfoil are also lower throughout the AOA range and these have all been due to the more complicated wind dynamics of a VAWT blade. 3.3.4. Flow visualizations Looking into the vorticity proﬁle of the ﬂuid space surrounding the blades gave insights into the phenomena happening for azimuths of interest over the VAWT rotation. In Fig. 18, a combined plot of the Q-criterion and z-vorticity detail ﬂow turbulence in the 3D and 2D domains, respectively. A single-value Q-criterion was rendered to visualize blade wake turbulence in 3D. The 2D zvorticity plot is inserted midway of the domain along the z-axis, cutting across the blades and post at z ¼ 0. Fig. 18 compares the vorticity proﬁles of the (a) cambered and (b) cambered TLE blades, which show striking contrast of wind ﬂow at blade wakes of blades at the azimuth angle of q ¼ 105 , approximately point 4 or q ¼ 106 in the torque, lift and drag plots, which was noted with the lowest torque value for the cambered TLE blade. At the speciﬁed azimuth, the cambered blade vorticity proﬁle shows streamlined ﬂow instead of vortex generation at the blade wake as observed with the cambered TLE blade. Behind the cambered TLE blade are explicitly massive vortices the size of the chord emanating from just before its trailing edge. Besides experiencing the maximum negative torque, it is also this time that the cambered TLE blade approximately experiences the peak drag coefﬁcient. This vortex proﬁle of the cambered TLE blade proliferates until the azimuth angle of q ¼ 180 or point 5, therewith the large vortices have fully disintegrated, and ﬂow has again become streamlined like that of the cambered blade. Thus, at the same Q-criterion vortical scale, the TLE blade has been shown to generate vortices severely increasing the ﬂow-induced drag and consequently. Reducing the blade torque. There is remarkable similarity of blade wakes in both blade types between q ¼ 345 and q ¼ 225 . This is the result of both blades having the same net torque and lift coefﬁcient values between q ¼ 180 to q ¼ 360 or points 5 to 1. Besides generating blade wake vortices, the TLE modiﬁcation affects vortex shedding as depicted by the altered vortex street in the z-vorticity proﬁle. The altered vortex shedding likewise poses blade torque reduction effects as evidenced by the reduced cambered TLE torque blade at the azimuth angle q ¼ 269 . Zoom-ins into the z-vorticity proﬁle at blade level in Fig. 19 illustrate the blade and ﬂuid interactions that cannot be given focus in Fig. 18. For instance, at the azimuth angle of q ¼ 0 , attached ﬂow can be observed among all three blades and that the ﬂow ﬁelds along the blade leading edges of both crest and trough of the cambered TLE blade are more apparent than that of the cambered blade. The same ﬂow ﬁeld grows more at the azimuth angle of q ¼ 55 , at which ﬂow separation from the trailing edge slightly creeps into the airfoil pressure side of the TLE trough location and the phenomenon progresses towards the azimuth angle of q ¼ 75 . At the TLE crests, over the range between these last two azimuth angles, blade vorticities are markedly the same with that of the cambered blade. It is therefore suggestive that the torque reduction observed with the TLE blade between the azimuthal period q ¼ 55 and q ¼ 75 is due to the TLE surface on the leading edge of blade inducing ﬂow separation. From q ¼ 75 to q ¼ 105 , when the TLE blade torque moves to its maximum negative value, the creeping ﬂow separation at the TLE trough location fully develops. And while at the TLE crest location turbulence is observed, ﬂow in this location remains attached. Distinctly, the turbulence observed at the TLE trough location is massive enough to be as long as the blade chord length. Given ﬂow remains attached at the TLE crest, turbulence in this part is the spillover of the turbulence formed at the trough section. Fluid ﬂow between two crests was contained e spanwise restriction of ﬂow e and generated turbulence that led to the wake vortices and detachment of ﬂow from the blades. 3.3.5. TLE performance at different TSR settings At the different TSR values, the torque output of the cambered Fig. 18. Vorticity plots using z-vorticity slice at z ¼ 0 and Q-criterion iso-surface of the (a) cambered and (b) cambered TLE VAWTs showing the azimuth of q ¼ 105 , the moment nearest to the lowest torque value of 3.59Nm at q ¼ 106 for the cambered TLE VAWT blade. ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan Fig. 19. Vorticity plots of the cambered TLE and cambered blades for selected azimuth angles. 289 290 ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan TLE VAWT changed accordingly. The individual blade torques, and net blade torques of the cambered TLE VAWT at the different TSR settings are presented in Figs. 20 and 21, respectively. In the charts, the shift in peak TSR to l ¼ 5 of the cambered TLE blade has its individual and net torque blade values assuming the torque curve proﬁles like those of the cambered blade at the peak TSR l ¼ 4. On average, the cambered TLE VAWT net blade torque values are lower than that of the cambered VAWT blade by 2.33Nm, thus its lower performance coefﬁcient of CP ¼ 0.10. The shift does not translate to any performance improvement and suggests increasing the wind stream velocity at inlet for optimal ﬂow. 4. Conclusion Using CFD, the performance of a 5 kW three-bladed H-rotor Darrieus VAWT with cambered TLE NACA 0025 blades was established. 3D VAWT models were generated and simulations ran using CAD and CAE software. Thereafter, the VAWT and blade ﬂow physics were discussed in detail using post-processing analyses integrating ﬂow visualizations with torque analyses, and lift and drag characterization. Transient steady wind ﬂow simulations using the k-u SST turbulence model required 10 complete VAWT rotations each to arrive at converged results. Coefﬁcients of lift, drag, and moment on all three blades were individually monitored throughout the simulations. Prior the main objective of performance study, the 3D model was validated against a transitional baseline 2D model, which itself was validated against reference studies in lieu of experimental validation. Using the baseline 2D model, optimal wall yþ setting was found to be yþ ¼ 0.1. Node density and time step parametric studies yielded a ﬁnal 2D model with a mesh consisting of a mixedcell rotor sub-grid with fully structured O-grid control circles around the blades, and a quad-dominant unstructured cell mesh from beyond the control circles into the farﬁeld sub-grid, running at a time step equivalent to q ¼ 1. The 3D equivalent is mixed-cell as well, with unstructured volume meshes around the extruded 2D O-grid control circles. Performance curves of both the baseline 2D Fig. 20. Blade torques (Tb) of the cambered TLE VAWT at different TSR settings. Fig. 21. Blade torques (Tb) of the cambered TLE VAWT at different TSR settings. and 3D models showed agreement to reference data despite coarseness of the 3D meshes, which are at least 26 times more populated than the baseline 2D mesh. Torque values of coincident blades for each of the cambered and cambered TLE VAWTs were shown to deviate throughout a full converged rotation. The cambered TLE blade behaving similarly with the cambered blade up to 55 azimuth has earlier onset of torque reversal at 74 azimuth shown to be caused by the changes in magnitude and vector of lift and drag forces, and suppression of torque reaching negative values up to 3.59Nm at 106 azimuth due to reduced lift forces and increased drag forces. The drag force overturns the blade rotation. Vorticity plots of the Q-criterion showed the cambered TLE blade at the moment of lowest torque value at 106 azimuth generating massive vortices the size of the blade chord from just before the trailing edge against the streamlined ﬂow of the cambered blade at the same instance. Flow separation reached halfway through the blade chord length from the trailing edge at this point for the cambered TLE blade as shown by the blade-level z-vorticity plot. While ﬂow separation already creeps in at the blade trailing edge at 75 azimuth, ﬂow at the TLE crests remains attached. Turbulence generated at the cambered TLE blade troughs then become massive enough to spillover to its crests, giving rise to the vortices and ﬂow detachment, all of which relate to ﬂow degradation. Lowering the lift and increasing drag reversed the net moment on the blade, thus the hysteresis loops of the lift and drag coefﬁcient plots against the AOA. An altered vortex street across the cambered TLE VAWT past the VAWT post encountered by the blade further degraded the performance downwind. The cycle-averaged blade torque of the cambered TLE VAWT is 0.24Nm, which is a quarter of that of the cambered VAWT. The reduction is primarily due to the tubercle curvature at the leading edge causing large negative torque values upwind of the cambered TLE VAWT. As a passive motion control structure, the TLE designed for the cambered NACA 0025 three-bladed H-rotor Darrieus VAWT has been detrimental to ﬂow that translates to poor performance. The net blade torque over one rotation of the TLE VAWT at the peak ~ o, L.A.M. Danao / Energy 175 (2019) 278e291 I.C.M. Lositan TSR is only 9.28 W of blade power. For the available wind power of PW ¼ 137.8 W, the cambered TLE VAWT has a performance coefﬁcient of CP ¼ 0.07 whereas the cambered VAWT has CP ¼ 0.30. Peak performance of the former also shifted to TSR l ¼ 5 but without signiﬁcance. The detrimental effects of TLE to the VAWT in study is speciﬁc to the VAWT design and operating conditions set and remains conﬁned to this study. Restated, this study identiﬁed speciﬁc parameters such as geometric conﬁgurations, and ﬂow and running conditions detrimental to ﬂow and performance of a VAWT with cambered TLE blades, but in no way does it discredit other researches, more signiﬁcantly of those TLE application studies on VAWTs herein presented. This study showed the TLE, designed based on recommendations from reference studies, to negate the performance of a three-bladed H-rotor Darrieus VAWT initially improved with the incorporation of cambering in its NACA 0025 airfoil blades and operating at the TSR range of l ¼ 3.5 to l ¼ 5 with l ¼ 4 as peak TSR. The VAWT operates at high TSR values accepting a steady wind stream of U ¼ 5 m/s, which are realistic values for wind ﬂow conditions yielding acceptable VAWT performance efﬁciencies. The study builds on previous TLE application studies on VAWTs. It identiﬁes the need for parametric studies including but not limited to design, conﬁguration and operating conditions of a VAWT with cambered TLE blades. Pursuit of further parametric studies is tantamount to the use of computational resources beyond capacity of the current computing setup and thus should form a part of a future endeavor. The study also highlights a CFD performance study procedure replicable on other alternate VAWT conﬁgurations with blade motion control structures. The procedure further stands out in its use of 2D model results as benchmarks for the 3D model, optimizing the 3D model from parametric studies on a 2D model, and investigating the inherent VAWT ﬂow characteristics with vorticity plots of the Q-criterion and z-vorticity integrated with the detailed torque analyses, and lift and drag characterization. Acknowledgment This work was supported in part by the Department of Science and Technology of the Republic of the Philippines through a research grant of its Engineering Research and Development for Technology (ERDT) Program. Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.energy.2019.03.033. 291 References [1] Timmer WA, Bak C. Aerodynamic characteristics of wind turbine blade airfoils. In: Brøndsted P, Nijssen RPL, editors. Advances in wind turbine blade design and materials. Cambridge, UK: Woodhead Publishing Limited; 2013. [2] Howell R, Qin N, Edwards J, Durrani N. Wind tunnel and numerical study of a small vertical axis wind turbine. In: Renewable energy, vol. 35. Elsevier Ltd; 2010. p. 412e22. [3] Hansen KL. Effect of leading edge tubercle on airfoil performance. PhD thesis. The University of Adelaide; 2012. [4] Aftab SMA, et al. Mimicking the humpback whale: an aerodynamic perspective. 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