Aerodynamic Design and Performance Analysis of a Micro-Scale Horizontal Axis Wind Turbine Blades along with endplate addition through multi-fidelity computational fluid dynamics tools

Aerodynamic Design and Performance Analysis of a Micro-Scale Horizontal Axis Wind Turbine Blades along with endplate addition through multi-fidelity computational fluid dynamics tools Néstor Alcañiza,Pau Varelaa,∗,Pedro Quinteroaand Roberto Navarroa aCMT - Clean Mobility & Thermofluids. Universitat Politècnica de València, Camino de Vera, s/n, Valencia, E-46022, Spain ARTICLE INFO Keywords: Aerodynamics Micro-scale Wind Turbine Computational Fluid Dynamics Blade Element Momentum Theory QBlade Endplate ABSTRACT The transition toward renewable energy sources has positioned wind energy as a critical technology for achieving global carbon neutrality targets. While large-scale wind farms dominate current installations, micro-scale horizontal-axis wind turbines present significant potential for distributed energy generation in remote and rural areas. This study presents a comprehensive methodology for designing micro-scale wind turbine blades through comparative analysis of three computational approaches: classical Blade Element Momentum Theory (BEMT), QBlade software, and Computational Fluid Dynamics (CFD) simulations, selecting the designing methodology based on a trade - off between accuracy and computational cost. A numerical campaign on airfoil assessment was conducted to identify optimal blade geometries, with performance evaluated based on power coefficient distribution, peak power output, and cut-in wind speed. The investigation reveals that CFD simulations predict 23.34% higher power coefficients at peak compared to BEMT and 22.46% compared to QBlade due to threedimensional effects including rotational stall delay. The addition of endplates to the optimized blade design demonstrates significant improvements in performance. This multi-fidelity approach provides a robust framework for micro-scale wind turbine design, balancing computational efficiency with accuracy requirements, and studies the impact of adding endplates. 1. Introduction1 The global imperative for carbon emission reduction2 has accelerated the deployment of renewable energy tech-3 nologies. In this global context wind energy presents itself4 as a key factor for achieving international climate targets.5 The Paris Agreement of 2015 established the goal of lim-6 iting global temperature increase to well below 2°C above7 pre-industrial levels [1], subsequently strengthened by the8 Glasgow Climate Pact in 2021, which aims for a 1.5°C9 limit [2]. To meet these targets, countries worldwide have10 committed to a decarbonization goal, with China targeting11 carbon neutrality by 2060 [3] and the European Union by12 2050 [4] among others.13 Wind energy capacity has recently experienced a contin-14 uous growth, with global installations continuing to expand15 both onshore and offshore [5]. However, the benefits of16 wind energy must extend beyond large-scale centralized17 wind farms in order to encompass distributed generation18 systems that can serve remote and rural communities with19 a lack of access to the centralized electrical grid or ade-20 quate infrastructure for large-scale installations. Micro-scale21 horizontal-axis wind turbines (HAWT), commonly defined22 by a rated power output below 1.5 kW [6], represent a critical23 component of this distributed energy strategy, even being24 able to be combined with other renewable energy sources25 such as solar panels [7].26 ∗Corresponding author [email protected] (N. Alcañiz); [email protected] (P. Varela); [email protected] (P. Quintero); [email protected] (R. Navarro) ORCID(s): 0009-0002-3285-8055 (N. Alcañiz); 0000-0002-7909-4569 (P. Varela); 0000-0003-4373-2079 (P. Quintero); 0000-0003-2587-4954 (R. Navarro) The design philosophy for micro-scale wind turbines 27 fundamentally differs from their large-scale counterparts, 28 emphasizing modularity, simplicity, and reduced mainte29 nance requirements. Traditional pitch control systems, while 30 effective for large turbines, introduce complexity and costs 31 that are often prohibitive for small installations. Conse32 quently, passive optimization strategies focusing on aerody33 namic blade design combined with electrical control sys34 tems such as Maximum Power Point Tracking (MPPT) have 35 become the preferred approach [8]. The implementation of 36 this control method must be coupled with a sufficiently wide 37 operational range of maximum or near-maximum efficiency 38 to avoid losses associated with reduced efficiency [9]. These 39 systems maximize power extraction by regulating the work40 ing tip speed ratio through generator control, eliminating the 41 need for complex mechanical pitch mechanisms. 42 The aerodynamic design of micro-scale wind turbine 43 blades presents unique challenges that require careful con44 sideration of computational methods and their inherent lim45 itations. The classical Blade Element Momentum Theory 46 (BEMT)hasbeenthe cornerstoneofwindturbinedesigndue 47 to its computational efficiency and reasonable accuracy, be48 ing extensively used in the literature where several different 49 authors use this method in order to optimize the chord and 50 twist distribution along the blade [10,11], since it has been 51 proven to improve the wind turbine performance respect a 52 non-optimized blade [12]. However, BEMT fundamental as53 sumptionoftwo-dimensional flowneglectssignificantthree54 dimensional effects that can impact the wind turbine perfor55 mance. Recent advances in computational tools have pro56 vided alternatives to traditional BEMT approaches aiming 57 to increase the studying fidelity of those three-dimensional 58 N.Alcañiz et al.: Preprint submitted to Elsevier Page 1 of 12 Micro-scale HAWT Blade Design effects. For instance, the open-source wind turbine design59 software QBlade [13] incorporates corrections for three-60 dimensional effects while maintaining computational effi-61 ciency. For that reason, QBlade has recently started to be62 used in the literature as a design tool [14,15] and vali-63 dated comparing the results obtained respect to the classical64 BEMT and experimental data [16,17]. The corrections65 included by this software address some of the limitations66 of classical BEMT by incorporating boundary layer analysis67 and rotational effects into the momentum theory framework68 [18]. For cases requiring higher fidelity, three-dimensional69 Computational Fluid Dynamics (CFD) simulations can be70 used in order to capture complex phenomena such as ro-71 tational stall delay, tip vortex formation, and blade-wake72 interactions[12,19,20].Thesemethodologiesareoftenused73 in the design process [21,22], allowing to create an optimum74 design.75 The reduced scale of the micro-scale wind turbines al-76 lows different methods of improving aerodynamic perfor-77 mance to be proposed, such as surface treatments [23],78 combining wind turbines in tandem configuration [24] or79 different blade tip designs relative to the bigger-scale options80 such as backwards or forwards swept blades [25] and the81 design of different kind of winglets [26,27]. Particularly,82 endplates (the simplest version of a winglet) have been also83 studied in the case of vertical-axis wind turbines [28].84 Yet, to the author’s knowledge, the literature does not85 address the endplates impact in the case of a horizontal-86 axis wind turbine, being the endplates a feature that could87 increase the aerodynamic performance of HAWTs without88 increasing significantly their manufacturing or design costs.89 While the literature examines the differences between90 the analysis methods presented [29,30], it is necessary to91 determine a trade-off between their fidelity and computa-92 tional cost in order to establish an efficient yet functional de-93 sign methodology, aiming to capture the three-dimensional94 effects. The present study addresses the critical need for95 a comprehensive design methodology that systematically96 compares these computational approaches while optimizing97 blade geometry for micro-scale HAWTs.98 This work develops a multi-fidelity design framework99 comparing BEMT,QBlade,and CFD methodologies.Within100 this framework, a systematic optimization of blade geometry101 is conducted through a numerical campaign. The study102 also focuses on the quantification of the three-dimensional103 effects on performance predictions. Finally, effectiveness of104 endplates will be investigated as a strategy for aerodynamic105 performance enhancement.106 This article first describes the implementation of the107 BEMT methodology and its three-dimensional corrections108 in subsection 2.1. Next, the CFD model set up and its mesh-109 ing and validation are addressed in subsection 2.2. Then,110 the followed design procedure, starting with the comparison111 of the different computational methods used and finally112 the effects of the endplates on the blade performance are113 presented in section 3. Finally, some concluding remarks are114 provided in section 4.115 2. Methodology 116 The design and analysis procedures outlined in this study 117 employ various numerical methodologies whose proper con118 figuration and implementation are critical for ensuring re119 liable results. This section presents the detailed setup and 120 procedures employed for each computational approach. 121 As it is observed in Figure 1, the design process is 122 divided in different steps. The design and analysis method123 ologies are described in subsection 2.1 and subsection 2.2.124 Then, the methods are compared in subsection 3.1 and a 125 method is selected in order to compute the airfoil assessment 126 study, which is done in subsection 2.3. Finally, a geometry 127 is selected and the effects of adding an endplate are studied 128 in subsection 3.3.129 2.1. Blade Element Momentum Theory 130 Implementation 131 Thismethod discretizesthe rotorblades intoindependent 132 sections, each assumed to generate constant force on the 133 flow field. The theory employs two fundamental induction 134 factors: the axial induction factor (𝑎) and the rotational 135 induction factor (𝑎′), which, together with the air velocity 136 𝑈∞and the rotational speed, 𝜔𝑟, define the velocity triangle 137 experienced by each blade section, as observed in Fig138 ure 2, creating the relative velocity 𝑈𝑟𝑒𝑙. These parameters 139 are essential for determining the resultant angle of attack, 140 following established methodologies [31]. This approach 141 inherently neglects three-dimensional flow effects. Addi142 tionally, the implementation requires lift and drag coefficient 143 databases as functions of angle of attack for each of the blade 144 section studied. The angle of attack has been obtained for 145 this paper through XFoil [32], which calculates lift by means 146 of an inviscid linear-vorticity panel method, whereas drag 147 considers the viscous effects through a distributed source 148 model superimposed on the airfoil and wake geometry. 149 These databases allow to calculate the loads at each section. 150 To enhance accuracy, Prandtl tip loss and Glauert correc151 tions were implemented, aiming to account for finite blade 152 number effects and induction factors exceeding the critical 153 value 𝑎𝑐(usually defined as 1/3), respectively [31]. 154 Furthermore, other corrections aiming to model three155 dimensional effects can be added. QBlade [13], an open156 source wind turbine design and analysis platform, incor157 porates a three-dimensional correction to classical BEMT. 158 This correction employs boundary layer equation magnitude 159 analysis for high aspect ratio rotating blades under both 160 attached and separated flow conditions, yielding simpli161 fied equations that are integrated into BEMT computations 162 without significant computational cost increase [18]. This 163 software also allows to create 3D models of blades optimiz164 ing the chord and twist distributions based on the BEMT 165 method. 166 The classical BEMT and the QBlade implementation 167 both allow to asses the wind turbine performance by cal168 culating the power and torque coefficients, which are di169 mensionless values of power and torque, as a function of 170 tip speed ratio, a relation between the rotational and lineal 171 N.Alcañiz et al.: Preprint submitted to Elsevier Page 2 of 12 Micro-scale HAWT Blade Design Figure 1: Schematic representation of the followed workflow. Figure 2: Velocity triangle configuration established by BEMT methodology. speeds perceived by the blade tip. These coefficients are172 defined, respectively, in Equation 1 and Equation 2 and the173 tip speed ratio in Equation 3.174 𝐶𝑃=𝑊 1 2𝜌𝐴𝑈3 ∞ , 𝐶𝑄=𝑄 1 2𝜌𝐴𝑈2 ∞𝑟 , 𝜆 =𝜔𝑅 𝑈∞ . (1) (2) (3) 175 2.2. Computational Fluid Dynamics176 WhileCFD provides enhancedfidelityinthree-dimensional177 flow modeling compared to BEMT, this advantage comes178 at increased computational expense. For achieving this179 increase in fidelity, the full geometry must be solved in a180 three-dimensional manner, omitting hybrid models such as181 the actuator disk.The model set up and meshing strategy will182 be discussed and validated using a NREL reference case.183 2.2.1. CFD Simulation Setup184 Thecomputational fluid simulations areperformed using185 the software StarCCM+. Multiple control volumes were186 established to ensure well-defined computational domains,187 as illustrated in Figure 3 and Figure 4. The configuration188 for a three-bladed HAWT employs a third of a cylinder as189 the domain imposing periodic boundary conditions phased190 at 120◦, neglecting tower effects for computational simplifi191 cation. The fluid is modeled as dry air at sea level conditions. 192 The main factors affecting the turbine performance are 193 the wind speed and the turbine rotational speed. The desired 194 flow velocity is imposed as normal to the domain inlet, while 195 atmospheric pressure at sea level is imposed at the outlet, as 196 seen in Figure 4. The curved sides of the domain are estab197 lished as symmetry planes. This symmetry condition, while 198 not physically representative, is commonly employed to 199 simulate extended domains while avoiding wall interaction 200 effects [33]. Simulations are run considering a steady-state 201 approach, modeling the rotation of the wind turbine through 202 Moving Reference Frame (MRF) methodology, applied to 203 the innermost volume observed in Figure 3 and Figure 4.204 Domain dimensions were established to ensure convergence 205 by minimizing boundary condition influence on the region 206 of interest. 207 A segregated solver was employed given Mach num208 bers below 0.3, enabling incompressible flow assumptions. 209 Flow modeling utilized Reynolds-Averaged Navier-Stokes 210 (RANS) equations under steady-state conditions. The 𝑘−𝜔211 𝑆𝑆𝑇 turbulence model was selected based on the literature 212 [34,19]. The described methodology is consistent with 213 established practices [35]. 214 2.2.2. Mesh Generation 215 The domain is discretized using polyhedral cells. The 216 mesh includes a 1.4 mm global thickness prism layer mesh 217 consisting on seven layers as well as local refinements at 218 the blade surface and its surroundings, including the rotat219 ing region. The surface refinement consists on increasing 220 the maximum curvature allowed for the cells on the blade 221 surface to a value of 168 and imposing its cell size to be 222 a 1% respect to the cell size imposed on the global domain. 223 The volumetric controls can be seen in Figure 3 and Figure 4 224 and consist on reducing the cell size to a 15% of the global 225 N.Alcañiz et al.: Preprint submitted to Elsevier Page 3 of 12 Micro-scale HAWT Blade Design Figure 3: CFD simulation domain and refinement volumes (not scale) side view Figure 4: CFD simulation domain and refinement volumes (not scale) perspective view Mesh 1 Mesh 2 Mesh 3 Base Size [ m ] 0.24375 0.1875 0.15 𝐶𝑃[ - ] 0.3638 0.3681 0.3798 Error - 1.19 % 3.18 % Number of elements 2 × 1064 × 1068 × 106 Difference - 170.47 % 176.13 % Table 1 𝐺𝐶𝐼 study results. domain cell size for the outermost volume and to a 5% for226 the innermost one.227 Grid Convergence Index (𝐺𝐶𝐼) analysis was conducted228 to quantify the error relative to the asymptotic solution. This229 methodology involves multiple simulations with varying230 mesh densities in order to determine the order of approxi-231 mation of the solution and to establish appropriate base size232 for maintaining the desired error tolerance [36]. The results233 of these simulations can be seen in Table 1, the refinement234 rate chosen is 1.25. Both the error in power coefficient and235 the difference in number of elements are defined respect to236 the previous mesh.237 Asymptotic range validation of the obtained results can 238 be confirmed through the expression shown in Equation 4 239 [37], confirming the abatement of discretization error. 240 𝐺𝐶𝐼23 𝑟𝑟𝑝𝐺𝐶𝐼12 = 0.998 ∼ 1.(4) Based on the simulations results, the order of approxima241 tion of the solution can be calculated. Next, a desired error 242 of 5% is imposed. The required base cell size for keeping the 243 error within the desired range can be calculated, as described 244 in the literature [36], to be 0.178 meters. The final mesh, 245 consisting on 6 × 106cells, can be seen in Figure 5.246 While this analysis was performed for a representative 247 geometry, the calculated base size was applied to all simu248 lations due to the equivalent nature of the flow phenomena 249 across configurations. 250 In order to ensure proper wall resolution and mesh qual251 ity, a Wall Y+ and cell aspect ratio analysis is performed. 252 The distribution demonstrates values of Wall Y+ below 5 for 253 all cells and below 1 for the 57.42% of the cells, confirming 254 mesh adequacy according to established criteria [38]. In case 255 of the cell aspect ratio, all the cells have a value over 0.05, 256 having the 75.53% of the cells a value above 0.95. 257 2.2.3. CFD Model Validation 258 The validation of the CFD model was conducted us259 ing the NREL Phase VI rotor geometry. Scaled computa260 tional domains were defined to preserve consistent blade261 to-volume ratios, and prism-layer remeshing was applied 262 to ensure that the Wall Y+ values remained within the 263 recommended range. The selected experimental dataset cor264 responds to Sequence I, characterized by a series of wind 265 speeds ranging from 5 m/s to 24 m/s, a constant rotational 266 speed of 72 rpm, and zero yaw angle. This sequence was 267 selected since it represents the conditions studied in this 268 paper. Numerical calculations of the pressure coefficient 269 distribution along the blade chord at selected spanwise po270 sitions were compared against available experimental mea271 surements [39] at three different working tip speed ratios. 272 Defining the pressure coefficient as seen in Equation 5, the 273 comparisons are presented in Figure 6. The pressure coef274 ficient distributions along the chord calculated by the CFD 275 show the same tendencies of those measured experimentally, 276 demonstrating the capability of the CFD to properly estimate 277 the experimental data and tendencies at different working 278 conditions. 279 𝑐𝑃 𝑟𝑒𝑠𝑠𝑅𝑜𝑡 =𝑃−𝑃0 1 2𝜌[𝑈2 ∞+ (𝜔𝑟)2] .(5) In addition to the pressure coefficient distributions, the 280 power coefficient vs tip speed ratio curve was calculated 281 from the computational pressure coefficient data following 282 the procedure established in the experimental report [39]. 283 The results, which can be seen in Figure 7, show a similar 284 power coefficient distribution for the different calculation 285 N.Alcañiz et al.: Preprint submitted to Elsevier Page 4 of 12 Micro-scale HAWT Blade Design Figure 5: CFD mesh side view close-up to the interest zone. Additional close-ups to the blade refinement volume and prism layer (a) Pressure coefficient distribution along chord for 46.6% span (b) Pressure coefficient distribution along chord for 80% span Figure 6: Pressure Coefficient distribution along the chord for CFD and experimental calculations at different span % at 𝜆= 1.67, 𝜆= 4.02 and 𝜆= 8.04 methods. The most noticeable discrepancies appear in 𝜆=286 5.02 and 𝜆= 5.74, which are a 10.03% lower and a 9.45%287 higher respectively when calculated from the CFD extracted288 data.289 2.3. Numerical Campaign290 A numerical campaign was formulated to systematically291 evaluate all feasible design configurations. The campaign292 framework was structured to assess three primary perfor-293 mance criteria:294 •Peak power coefficient maximization.295 •Power coefficient distribution as a function of tip296 speed ratio, targeting low stall tip speed ratios, mean-297 ing a lower maximum rotational speed for a given298 wind speed, thus increasing overall security, while299 maintaining an adequate optimum operational range 300 to mitigate efficiency losses associated with Maxi301 mum Power Point Tracker (MPPT) system imperfec302 tions [9]. 303 •Torque coefficient at a tip speed ratio of zero, serving 304 as an indicator of cut-in wind speed. 305 The cut-in wind speed is calculated as shown in Equa306 tion 6 307 𝑉𝑐𝑖 =√2𝑄𝑐𝑖 𝜌𝐴𝑐𝑄𝑅,(6) N.Alcañiz et al.: Preprint submitted to Elsevier Page 5 of 12 Micro-scale HAWT Blade Design Figure 7: Power coefficient versus tip speed ratio curves for the NREL Phase VI blade geometry obtained using different calculation methods. where 𝑄𝑐𝑖 represents the generator starting torque, assumed308 to be 0.5 Nm for this analysis. The torque coefficient 𝑐𝑄is309 determined at zero tip speed ratio according to Equation 7.310 𝑐𝑄=𝑄|𝜆=0 1 2𝜌𝐴𝑈2 ∞𝑅 .(7) The design variable will be the airfoil used along the311 span. The same airfoil will be used along the whole span, as312 commonly used in the design of micro-scale wind turbines313 [35,40]. The different airfoils are obtained from an airfoil314 database [41], filtering to obtain those designed specifically315 for wind turbines and a NACA0015, making a total of 33316 different airfoils. The selected families are the Bergey, Selig,317 Althaus, Martin-Hepperle, Jacobs, and Wortmann [42,43].318 The following design constraints were imposed to ensure319 practical feasibility:320 •Rotor radius of 0.8 m, representing a balance between321 compactness and power output capability (estimated322 maximum of 1 kW) [44].323 •Blade number as three, providing a compromise be-324 tween power extraction, operational stability, and325 manufacturing costs [45].326 •Design tip speed ratio as 3.0, selected to enhance low327 wind speed performance while reducing structural328 loading requirements [46].329 •Solidity at the root lower than one, established to330 prevent inter-blade interference given the tendency for331 chord increase at the root during optimization and332 achieved by imposing a chord at the root of 0.2 m.333 The chord and twist distributions along the span for the334 different geometries are not considered a variable since will335 be optimized based on the BEMT method.336 Figure 8: Power coefficient versus tip speed ratio curves for the Bergey blade geometry obtained using different computational methods 3. Results 337 This section presents the results obtained through the 338 different methodologies employed in this study. Initially, 339 a comparative analysis between computational methods is 340 conducted to establish the most suitable approach for the 341 numerical campaign. Subsequently, the campaign results 342 and associated analyses are presented and discussed. Finally, 343 endplates are implemented in the geometry aiming to im344 prove the blade performance. 345 3.1. Comparative Analysis of Computational 346 Methods 347 To evaluate the performance and computational cost of 348 the different approaches, a reference blade geometry based 349 on the Bergey BW-3 airfoil was selected for comparative 350 analysis. The power coefficient characteristics of this blade 351 were calculated using the three methodologies described in 352 the previous section. The comparative results are presented 353 in Figure 8.354 The observed discrepancies between the computational 355 methods can be attributed to three-dimensional flow ef356 fects, which are neglected by the BEMT and simplified by 357 QBlade. These effects result in significant differences in 358 the predicted power coefficient distribution and peak value: 359 23.34% between CFD and BEMT, and 22.46% between 360 CFD and QBlade, being the CFD the method presenting a 361 higher peak power coefficient. The three-dimensional flow 362 structures responsible for these discrepancies are visualized 363 in Figure 9.364 The three-dimensional effects observed are primarily 365 associated with the phenomenon of rotational stall delay, 366 whereby the airfoil stall condition is postponed due to cen367 trifugal and Coriolis forces acting on the rotating blade. This 368 mechanism has been demonstrated to be relevant in wind 369 turbine applications [47]. Figure 9, illustrates wall shear 370 stress streamlines with pressure coefficient colormap at the 371 design tip speed ratio (𝜆= 3.0). It is observed that the flow 372 N.Alcañiz et al.: Preprint submitted to Elsevier Page 6 of 12 Micro-scale HAWT Blade Design Figure 9: Wall shear stress streamlines with pressure coefficient colormap on the suction side of the Bergey blade at 𝜆= 3 detaches from the blade near the leading edge on the suction373 side, corresponding to the region of maximum suction, and374 reattaches at higher chord values. This behavior is associated375 with the formation of a recirculation zone, indicative of com-376 plex three-dimensional flow structures. Such flow features377 enhance suction, leading to higher power coefficients than378 those predicted by methods that neglect three-dimensional379 effects, as illustrated in Figure 8.380 From a computational cost perspective, the CFD simu-381 lations required an average of 27 hours to generate complete382 power coefficient curves when run on a 15-core cluster,383 representing a computational cost approximately 810 times384 higher than that of BEMT or QBlade, which completed the385 same calculations in approximately 2 minutes on average386 using an 8-core laptop.387 Considering the trade-off between computational accu-388 racy and cost, and acknowledging that the significance of389 three-dimensional effects has been established, QBlade was390 selected as the primary computational tool for the numerical391 campaign on turbine blade airfoil assessment. This decision392 was based on its substantially lower computational cost393 compared to CFD, while still considering three-dimensional394 effects, albeit in a simplified form.395 3.2. Numerical Campaign Results and Analysis396 A numerical campaign to evaluate the suitability of397 33 different airfoils for the design of turbine blades was398 conducted using QBlade, according to the methodology399 described in section 2.400 Based on the selection criteria established in the method-401 ology section, the three highest-performing geometries were402 identified from the campaign results. These candidate con-403 figurations demonstrate superior aerodynamic performance404 characteristics based on the criteria previously established,405 as illustrated in Figure 10.406 The airfoil profiles corresponding to each candidate ge-407 ometry are presented in Figure 11. It should be noted that408 the blade nomenclature refers to the airfoil family employed409 in each design configuration.410 Figure 10: Power coefficient versus tip speed ratio curves for the three selected candidate geometries Figure 11: Airfoil profiles of the three numerical campaign candidate geometries 3.2.1. Cut-in Wind Speed Analysis 411 The remaining performance criterion evaluated for the 412 candidate geometries is the cut-in wind speed, with prefer413 ence given to configurations exhibiting the lowest values. 414 The lowest cut-in speed was achieved by the Jacobs 415 blade, featuring a USNPS4 airfoil, with 3.10 m/s. The high416 est cut-in speed was the Selig blade, featuring a SG6041 417 airfoil and a value of 3.59 m/s. The Bergey blade, consisting 418 of the BW-3 airfoil, achieved a cut-in speed of 3.12 m/s. 419 3.2.2. Final Geometry Selection 420 Followingcomprehensiveevaluationof the aerodynamic 421 performance metrics and cut-in wind speed characteristics, 422 the Bergey blade configuration emerges as the selected de423 sign candidate. This selection is justified by its performance 424 characteristics, including the lowest stall tip speed ratio, a 425 similar peak power coefficient respect to the other candi426 dates, and competitive cut-in wind speed performance. 427 N.Alcañiz et al.: Preprint submitted to Elsevier Page 7 of 12 Micro-scale HAWT Blade Design Figure 12: Chord and twist distributions along the span of the Bergey blade Figure 13: Endplate geometric specifications The optimized chord and twist distributions along the428 blade span, obtained through QBlade BEMT-based opti-429 mization algorithm, are presented in Figure 12. These dis-430 tributions represent the geometric parameters that maxi-431 mize aerodynamic efficiency while satisfying the design432 constraints imposed during the optimization process.433 3.3. Effects on Performance due to Endplate434 Addition435 Endplates are flat surfaces attached to the blade tip. Their436 main objective is to prevent the formation of recirculation437 vortexes at the blade tip, thereby increasing the torque gen-438 eration and consequently improving the power coefficient.439 To enhance the fidelity of the computational simulations,440 additionalgeometricfeaturesincludingahemisphericalnose441 and a cylindrical nacelle were incorporated into the model.442 Preliminary analysis confirmed that these features have neg-443 ligible impact on the calculated power coefficient curves,444 while providing a more realistic representation of the com-445 plete turbine geometry.446 The chosen endplate is illustrated in Figure 13.447 The aerodynamic impact of the endplate implementation448 on the power coefficient characteristics is presented in Fig-449 ure 14. The results demonstrate significant modifications in450 Figure 14: Power coefficient versus tip speed ratio curves for Bergey blade with different wingtip configurations the turbine operational behavior across different tip speed 451 ratios. 452 The most notable effect observed is the increase of the 453 negative slope in the power coefficient curve for tip speed 454 ratios exceeding the design value. This characteristic is 455 advantageous from a safety perspective, as it reduces the 456 maximum achievable rotational velocity. Additionally, the 457 endplate configuration results in an increase in the peak 458 power coefficient of a 2.3%. The increase in peak power 459 coefficient provided by the endplate is of the same order 460 of magnitude as other tip treatments reported in the litera461 ture [25,26]. However, the effects on the power coefficient 462 distribution are not observed with other types of wingtip 463 configurations. Regarding the cut-in speed there are not 464 relevant changes. It is important to consider that adding an 465 endplate would mean an increase of inertia, so the cut-in 466 speeds could be increased. 467 In order to determine the reasons behind the increase in 468 peak power coefficient, several flow analysis are performed. 469 Firstly, the torque coefficient along the radius is shown in 470 Figure 15, indicating an increase in the torque generated 471 towards the tip when adding the endplate. 472 The enhanced torque generation is further corroborated 473 by the pressure coefficient distribution analysis on the blade 474 suction surface, as shown in Figure 16, where an increase in 475 suction can be observed. 476 The observed improvements in both pressure coefficient 477 andtip torquegenerationare attributed to theendplate ability 478 to suppress tip vortex formation at the blade tip, effectively 479 relocating the vortical structures to the upper region of the 480 endplate. This phenomenon can be visualized through wall 481 shear stress streamlines superposed to the pressure coeffi482 cient distribution already shown, as presented in Figure 17,483 where it is shown how the flow is attach for the whole blade 484 when adding an endplate. 485 Thesevisualizationsdemonstratethatthe endplate size is 486 a critical factor in its performance. Undersizing the endplate 487 could result in decreased efficiency due to the proximity 488 N.Alcañiz et al.: Preprint submitted to Elsevier Page 8 of 12 Micro-scale HAWT Blade Design Figure 15: Spanwise distribution of torque coefficient for different wingtip configurations at 𝜆= 3 Figure 16: Pressure coefficient distribution at the tip of the blade suction side with (left) and without (right) endplate at 𝜆= 3 of tip vortices to the blade surface, negatively impacting489 aerodynamic performance. Conversely, oversizing the end-490 plate could introduce unnecessary structural loads due to491 increased weight without providing additional aerodynamic492 benefits, as the tip vortex effects on the blade would remain493 unchanged.494 The modification in power coefficient vs. tip speed ratio495 distribution can be explained through flow physics analysis.496 In the baseline configuration without endplates, flow recir-497 culation around the blade tip enhances the radial velocity498 component. The endplate implementation suppresses this499 recirculation, consequently reducing the radial flow com-500 ponent. At elevated tip speed ratios, flow separation occurs501 at the nose region, generating vortical structures. The re-502 duced radial flow component allows the vortical structures503 to develop and extend until reaching the blade pressure side,504 negatively affecting the blade performance, as illustrated in505 Figure 18.506 Figure 17: Wall shear stress streamlines with pressure coefficient colormap at the tip of the blade suction side with (left) and without (right) endplate at 𝜆= 3 Figure 18: Velocity magnitude colormap with streamlines in spanwise view at 𝜆= 7 for configurations without (top) and with (bottom) endplate 4. Concluding Remarks 507 This study presents an original comprehensive method508 ology for the design and analysis of micro-scale horizontal509 axis wind turbines blades, demonstrating the critical im510 portance of computational method selection and three511 dimensional effects consideration in achieving optimal aero512 dynamic performance. 513 The systematic comparison of the traditional BEMT 514 formulation, QBlade, and CFD methodologies reveals sig515 nificant performance prediction differences, with CFD sim516 ulations indicating 23.34% higher power coefficients com517 pared to classical BEMT and 22.46% compared to QBlade. 518 This disparity stems from three-dimensional effects, partic519 ularly rotational stall delay, which are inadequately captured 520 by two-dimensional assumptions inherent in BEMT. The 521 N.Alcañiz et al.: Preprint submitted to Elsevier Page 9 of 12