Effects of a J-Shaped Blade on the Performance of a Vertical-Axis Wind Turbine Using the Improved Delayed Detached Eddy Simulation Method
Abstract
1. Introduction
2. Physical Model and Numerical Method
2.1. Baseline Solver
2.2. Turbulence Modeling
2.2.1. Shear Stress Transport Model
2.2.2. Improved Delayed Detached Eddy Simulation
2.3. Geometry and Flow Condition
2.4. Computational Mesh and Numerical Setup
2.5. Validation
3. Results and Discussion
3.1. Aerodynamic Loads
3.2. Pressure Distributions
3.3. Flow Field Structures
4. Conclusions
- At TSR = 1, the J-shaped blade exhibited a peak CM approximately 13.5% higher and an average CM about 7% higher than the S-shaped blade. The peak CL during dynamic stall was also increased by approximately 11% compared to the S-shaped blade. At TSR = 1.6, the J-shaped blade continued to improve performance, with the peak CM and peak CL increased by 1.8% and 1.5%, respectively, although the improvements were less pronounced than at a lower TSR. Furthermore, the onset of dynamic stall was delayed by approximately 4° to 6° in azimuth for the J-shaped blade under low and medium TSR conditions. These results indicate that the principal positive effect on the enhanced power coefficient of the J-shaped blade is primarily observed in the dynamic stall region. The J-shaped blade exhibited a higher lift coefficient within the stall region, which provides a more substantial positive contribution to the tangential force, enhancing the torque and power coefficients.
- The J-shaped blade exhibited a larger negative pressure zone at the leading edge, increasing the pressure difference between the pressure and suction sides, which boosts the lift coefficient. Moreover, the J-shaped blade had a less pronounced suction zone at the blade tip compared to the S-shaped blade, resulting in a smaller pressure difference between the blade root and tip. Consequently, the cross-flow on the blade surface was weaker, which makes it less prone to flow separation.
- When a wind turbine blade undergoes dynamic stall, the tip vortex interacts with the dynamic stall vortex, forming an -shaped vortex on the blade’s suction side. This -shaped vortex signifies the blade tip vortex’s inhibiting effect on the generation and development of the dynamic stall vortex. Compared to the S-shaped blade, the J-shaped blade generated a stronger tip vortex, which more effectively suppressed the dynamic stall vortex. Consequently, the J-shaped blade exhibited superior performance in suppressing flow separation and delaying dynamic stall.
- After the tip vortex and dynamic stall vortex detached from the blade surface, a wake region was formed, which had a detrimental impact on the wind turbine blades. The wake region vortices of the J-shaped VAWT were significantly fewer than those of the S-shaped VAWT, allowing for the J-shaped blade to recover more quickly from the negative effects of the wake region.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Symbols | Abbreviations | ||
A | swept area of the rotor (m2) | 3D | Three-dimensional |
c | chord length (m) | CFD | Computational Fluid Dynamics |
CD | drag coefficient | DDES | Delayed Detached Eddy Simulation |
CL | lift coefficient | DES | Detached Eddy Simulation |
CM | torque coefficient | HAWT | Horizontal Axis Wind Turbine |
CP | power coefficient | IDDES | Improved Delayed Detached Eddy Simulation |
CT | tangential force coefficient | L.E. | leading edge |
D | turbine diameter (m) | LES | Large Eddy Simulation |
M | rotor torque (Nm) | LU-SGS | Lower-Upper Symmetric Gauss-Seidel |
incoming flow velocity (m/s) | MPI | Message Passing Interface | |
W | the relative velocity of the blades (m/s) | SST | Shear Stress Transport |
dimensionless wall distance | T.E. | trailing edge | |
TSR | Tip Speed Ratio | ||
Greek | URANS | Unsteady Reynolds Averaged Navier-Stokes | |
angle of attack () | VAWT | Vertical Axis Wind Turbine | |
pitch angle () | |||
azimuthal angle () | |||
tip speed ratio | |||
incoming flow density (kg/m3) | |||
rotational angular velocity (rad/s) | |||
vorticity (1/s) | |||
dimensionless vorticity |
References
- Evans, A.; Strezov, V.; Evans, T.J. Assessment of Sustainability Indicators for Renewable Energy Technologies. Renew. Sustain. Energy Rev. 2009, 13, 1082–1088. [Google Scholar] [CrossRef]
- Ismail, M.F.; Vijayaraghavan, K. The Effects of Aerofoil Profile Modification on a Vertical Axis Wind Turbine Performance. Energy 2015, 80, 20–31. [Google Scholar] [CrossRef]
- Rezaeiha, A.; Kalkman, I.; Blocken, B. Effect of Pitch Angle on Power Performance and Aerodynamics of a Vertical Axis Wind Turbine. Appl. Energy 2017, 197, 132–150. [Google Scholar] [CrossRef]
- Buchner, A.-J.; Soria, J.; Honnery, D.; Smits, A.J. Dynamic Stall in Vertical Axis Wind Turbines: Scaling and Topological Considerations. J. Fluid Mech. 2018, 841, 746–766. [Google Scholar] [CrossRef]
- Rolin, V.F.-C.; Porté-Agel, F. Experimental Investigation of Vertical-Axis Wind-Turbine Wakes in Boundary Layer Flow. Renew. Energy 2018, 118, 1–13. [Google Scholar] [CrossRef]
- Kumar, R.; Raahemifar, K.; Fung, A.S. A Critical Review of Vertical Axis Wind Turbines for Urban Applications. Renew. Sustain. Energy Rev. 2018, 89, 281–291. [Google Scholar] [CrossRef]
- Tjiu, W.; Marnoto, T.; Mat, S.; Ruslan, M.H.; Sopian, K. Darrieus Vertical Axis Wind Turbine for Power Generation II: Challenges in HAWT and the Opportunity of Multi-Megawatt Darrieus VAWT Development. Renew. Energy 2015, 75, 560–571. [Google Scholar] [CrossRef]
- Hohman, T.C.; Martinelli, L.; Smits, A.J. The Effects of Inflow Conditions on Vertical Axis Wind Turbine Wake Structure and Performance. J. Wind. Eng. Ind. Aerodyn. 2018, 183, 1–18. [Google Scholar] [CrossRef]
- Hand, B.; Cashman, A. Aerodynamic Modeling Methods for a Large-Scale Vertical Axis Wind Turbine: A Comparative Study. Renew. Energy 2018, 129, 12–31. [Google Scholar] [CrossRef]
- Howell, R.; Qin, N.; Edwards, J.; Durrani, N. Wind Tunnel and Numerical Study of a Small Vertical Axis Wind Turbine. Renew. Energy 2010, 35, 412–422. [Google Scholar] [CrossRef]
- Paraschivoiu, I. Double-Multiple Streamtube Model for Studying Vertical-Axis Wind Turbines. J. Propuls. Power 1988, 4, 370–377. [Google Scholar] [CrossRef]
- Soraghan, C.E.; Leithead, W.E.; Feuchtwang, J.; Yue, H. Double Multiple Streamtube Model for Variable Pitch Vertical Axis Wind Turbines. In Proceedings of the 31st AIAA Applied Aerodynamics Conference, San Diego, CA, USA, 24–27 June 2013; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2013; p. 2802. [Google Scholar]
- Wang, L.B.; Zhang, L.; Zeng, N.D. A Potential Flow 2-D Vortex Panel Model: Applications to Vertical Axis Straight Blade Tidal Turbine. Energy Convers. Manag. 2007, 48, 454–461. [Google Scholar] [CrossRef]
- Wang, L.; Yeung, R.W. On the Performance of a Micro-Scale Bach-Type Turbine as Predicted by Discrete-Vortex Simulations. Appl. Energy 2016, 183, 823–836. [Google Scholar] [CrossRef]
- Mandal, A.C.; Burton, J.D. The Effects of Dynamic Stall and Flow Curvature on the Aerodynamics of Darrieus Turbines Applying the Cascade Model. Wind Eng. 1994, 18, 267–282. [Google Scholar]
- Le Fouest, S.; Mulleners, K. Optimal Blade Pitch Control for Enhanced Vertical-Axis Wind Turbine Performance. Nat. Commun. 2024, 15, 2770. [Google Scholar] [CrossRef]
- Simão Ferreira, C.; Van Kuik, G.; Van Bussel, G.; Scarano, F. Visualization by PIV of Dynamic Stall on a Vertical Axis Wind Turbine. Exp. Fluids 2009, 46, 97–108. [Google Scholar] [CrossRef]
- Van Der Deijl, W.; Obligado, M.; Sicot, C.; Barre, S. Experimental Study of Mean and Turbulent Velocity Fields in the Wake of a Twin-Rotor Vertical Axis Wind Turbine. J. Phys. Conf. Ser. 2022, 2265, 22073. [Google Scholar] [CrossRef]
- Buchner, A.-J.; Lohry, M.W.; Martinelli, L.; Soria, J.; Smits, A.J. Dynamic Stall in Vertical Axis Wind Turbines: Comparing Experiments and Computations. J. Wind. Eng. Ind. Aerodyn. 2015, 146, 163–171. [Google Scholar] [CrossRef]
- Barnes, A.; Marshall-Cross, D.; Hughes, B.R. Towards a Standard Approach for Future Vertical Axis Wind Turbine Aerodynamics Research and Development. Renew. Sustain. Energy Rev. 2021, 148, 111221. [Google Scholar] [CrossRef]
- Spalart, P.; Jou, W.-H.; Strelets, M.; Allmaras, S. Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach. In Proceedings of the First AFOSR International Conference on DNS/LES, Ruston, LA, USA, 4–8 August 1997; Greyden Press: Columbus, OH, USA, 1997; pp. 137–147. [Google Scholar]
- Spalart, P.R.; Deck, S.; Shur, M.L.; Squires, K.D.; Strelets, M.K.; Travin, A. A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities. Theoret. Comput. Fluid Dyn. 2006, 20, 181–195. [Google Scholar] [CrossRef]
- Shur, M.L.; Spalart, P.R.; Strelets, M.K.; Travin, A.K. A Hybrid RANS-LES Approach with Delayed-DES and Wall-Modelled LES Capabilities. Int. J. Heat Fluid Flow 2008, 29, 1638–1649. [Google Scholar] [CrossRef]
- Lei, H.; Zhou, D.; Bao, Y.; Li, Y.; Han, Z. Three-Dimensional Improved Delayed Detached Eddy Simulation of a Two-Bladed Vertical Axis Wind Turbine. Energy Convers. Manag. 2017, 133, 235–248. [Google Scholar] [CrossRef]
- Chen, J.; Chen, L.; Xu, H.; Yang, H.; Ye, C.; Liu, D. Performance Improvement of a Vertical Axis Wind Turbine by Comprehensive Assessment of an Airfoil Family. Energy 2016, 114, 318–331. [Google Scholar] [CrossRef]
- Huang, H.; Luo, J.; Li, G. Study on the Optimal Design of Vertical Axis Wind Turbine with Novel Variable Solidity Type for Self-Starting Capability and Aerodynamic Performance. Energy 2023, 271, 127031. [Google Scholar] [CrossRef]
- Ardaneh, F.; Abdolahifar, A.; Karimian, S.M.H. Numerical Analysis of the Pitch Angle Effect on the Performance Improvement and Flow Characteristics of the 3-PB Darrieus Vertical Axis Wind Turbine. Energy 2022, 239, 122339. [Google Scholar] [CrossRef]
- Singh, E.; Roy, S.; Yam, K.S.; Law, M.C. Numerical Analysis of H-Darrieus Vertical Axis Wind Turbines with Varying Aspect Ratios for Exhaust Energy Extractions. Energy 2023, 277, 127739. [Google Scholar] [CrossRef]
- Zhu, C.; Yang, H.; Qiu, Y.; Zhou, G.; Wang, L.; Feng, Y.; Shen, Z.; Shen, X.; Feng, X.; Wang, T. Effects of the Reynolds Number and Reduced Frequency on the Aerodynamic Performance and Dynamic Stall Behaviors of a Vertical Axis Wind Turbine. Energy Convers. Manag. 2023, 293, 117513. [Google Scholar] [CrossRef]
- Peng, H.Y.; Lam, H.F. Turbulence Effects on the Wake Characteristics and Aerodynamic Performance of a Straight-Bladed Vertical Axis Wind Turbine by Wind Tunnel Tests and Large Eddy Simulations. Energy 2016, 109, 557–568. [Google Scholar] [CrossRef]
- Xu, W.; Li, C.; Huang, S.; Wang, Y. Aerodynamic Performance Improvement Analysis of Savonius Vertical Axis Wind Turbine Utilizing Plasma Excitation Flow Control. Energy 2022, 239, 122133. [Google Scholar] [CrossRef]
- Shukla, V.; Kaviti, A.K. Performance Evaluation of Profile Modifications on Straight-Bladed Vertical Axis Wind Turbine by Energy and Spalart Allmaras Models. Energy 2017, 126, 766–795. [Google Scholar] [CrossRef]
- Ghafoorian, F.; Enayati, E.; Mirmotahari, S.R.; Wan, H. Self-Starting Improvement and Performance Enhancement in Darrieus VAWTs Using Auxiliary Blades and Deflectors. Machines 2024, 12, 806. [Google Scholar] [CrossRef]
- Attie, C.; ElCheikh, A.; Nader, J.; Elkhoury, M. Performance Enhancement of a Vertical Axis Wind Turbine Using a Slotted Deflective Flap at the Trailing Edge. Energy Convers. Manag. 2022, 273, 116388. [Google Scholar] [CrossRef]
- MacPhee, D.; Beyene, A. Recent Advances in Rotor Design of Vertical Axis Wind Turbines. Wind. Eng. 2012, 36, 647–665. [Google Scholar] [CrossRef]
- Bhuyan, S.; Biswas, A. Investigations on Self-Starting and Performance Characteristics of Simple H and Hybrid H-Savonius Vertical Axis Wind Rotors. Energy Convers. Manag. 2014, 87, 859–867. [Google Scholar] [CrossRef]
- Wakui, T.; Tanzawa, Y.; Hashizume, T.; Nagao, T. Hybrid Configuration of Darrieus and Savonius Rotors for Stand-Alone Wind Turbine-Generator Systems. Electr. Eng. Jpn. 2005, 150, 13–22. [Google Scholar] [CrossRef]
- Ghafoorian, F.; Hosseini Rad, S.; Moghimi, M. Enhancing Self-Starting Capability and Efficiency of Hybrid Darrieus–Savonius Vertical Axis Wind Turbines with a Dual-Shaft Configuration. Machines 2025, 13, 87. [Google Scholar] [CrossRef]
- Zamani, M.; Maghrebi, M.J.; Varedi, S.R. Starting Torque Improvement Using J-Shaped Straight-Bladed Darrieus Vertical Axis Wind Turbine by Means of Numerical Simulation. Renew. Energy 2016, 95, 109–126. [Google Scholar] [CrossRef]
- Zamani, M.; Nazari, S.; Moshizi, S.A.; Maghrebi, M.J. Three Dimensional Simulation of J-Shaped Darrieus Vertical Axis Wind Turbine. Energy 2016, 116, 1243–1255. [Google Scholar] [CrossRef]
- Mohamed, M.H. Criticism Study of J-Shaped Darrieus Wind Turbine: Performance Evaluation and Noise Generation Assessment. Energy 2019, 177, 367–385. [Google Scholar] [CrossRef]
- Pan, L.; Zhu, Z.; Xiao, H.; Wang, L. Numerical Analysis and Parameter Optimization of J-Shaped Blade on Offshore Vertical Axis Wind Turbine. Energies 2021, 14, 6426. [Google Scholar] [CrossRef]
- García Auyanet, A.; Santoso, R.E.; Mohan, H.; Rathore, S.S.; Chakraborty, D.; Verdin, P.G. CFD-Based J-Shaped Blade Design Improvement for Vertical Axis Wind Turbines. Sustainability 2022, 14, 15343. [Google Scholar] [CrossRef]
- Celik, Y.; Ingham, D.; Ma, L.; Pourkashanian, M. Design and Aerodynamic Performance Analyses of the Self-Starting H-Type VAWT Having J-Shaped Aerofoils Considering Various Design Parameters Using CFD. Energy 2022, 251, 123881. [Google Scholar] [CrossRef]
- Farzadi, R.; Bazargan, M. 3D Numerical Simulation of the Darrieus Vertical Axis Wind Turbine with J-Type and Straight Blades under Various Operating Conditions Including Self-Starting Mode. Energy 2023, 278, 128040. [Google Scholar] [CrossRef]
- Li, Q.; Sun, X.; Wang, G. Detached-Eddy Simulation of the Vortex System on the High-Lift Common Research Model. Phys. Fluids 2024, 36, 025173. [Google Scholar] [CrossRef]
- Wang, G.; Li, Q.; Liu, Y. IDDES Method Based on Differential Reynolds-Stress Model and Its Application in Bluff Body Turbulent Flows. Aerosp. Sci. Technol. 2021, 119, 107207. [Google Scholar] [CrossRef]
- Li, Q.; Chen, X.; Wang, G.; Liu, Y. A Dynamic Version of the Improved Delayed Detached-Eddy Simulation Based on the Differential Reynolds-Stress Model. Phys. Fluids 2022, 34, 115112. [Google Scholar] [CrossRef]
- Chen, X.; Wang, G.; Ye, Z. Wind Tunnel Wall Interference Correction for Transonic Airfoils with Data-Reduced Ensemble Kalman Filter. Phys. Fluids 2024, 36, 105139. [Google Scholar] [CrossRef]
- Wang, G.; Chen, X.; Xing, Y.; Zeng, Z. Multi-Body Separation Simulation with an Improved General Mesh Deformation Method. Aerosp. Sci. Technol. 2017, 71, 763–771. [Google Scholar] [CrossRef]
- Zhou, H.; Nie, M.; Qin, M.; Wang, G. An Unsteady Aerodynamic Reduced-Order Modelling Framework for Shock-Dominated Flow with Application on Shock-Induced Panel Flutter Prediction. J. Fluids Struct. 2025, 133, 104251. [Google Scholar] [CrossRef]
- Wang, G.; Ye, Z.-Y. Mixed Element Type Unstructured Grid Generation and Its Application to Viscous Flow Simulation. In Proceedings of the 24th International Congress of Aeronautical Sciences, Yokohama, Japan, 29 August–3 September 2004; p. 2004-2. [Google Scholar]
- Menter, F.R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA J. 1994, 32, 1598–1605. [Google Scholar] [CrossRef]
- Ferreira, C.S.; Geurts, B. Aerofoil Optimization for Vertical-Axis Wind Turbines. Wind Energy 2015, 18, 1371–1385. [Google Scholar] [CrossRef]
- Lei, H.; Su, J.; Bao, Y.; Chen, Y.; Han, Z.; Zhou, D. Investigation of Wake Characteristics for the Offshore Floating Vertical Axis Wind Turbines in Pitch and Surge Motions of Platforms. Energy 2019, 166, 471–489. [Google Scholar] [CrossRef]
- Lam, H.F.; Peng, H.Y. Study of Wake Characteristics of a Vertical Axis Wind Turbine by Two- and Three-Dimensional Computational Fluid Dynamics Simulations. Renew. Energy 2016, 90, 386–398. [Google Scholar] [CrossRef]
- Dessoky, A.; Lutz, T.; Bangga, G.; Krämer, E. Computational Studies on Darrieus VAWT Noise Mechanisms Employing a High Order DDES Model. Renew. Energy 2019, 143, 404–425. [Google Scholar] [CrossRef]
- Bravo, R.; Tullis, S.; Ziada, S. Performance Testing of a Small Vertical-Axis Wind Turbine. In Proceedings of the 21st Canadian Congress of Applied Mechanics, Toronto, ON, Canada, 3–7 June 2007; pp. 470–471. [Google Scholar]
- Daróczy, L.; Janiga, G.; Petrasch, K.; Webner, M.; Thévenin, D. Comparative Analysis of Turbulence Models for the Aerodynamic Simulation of H-Darrieus Rotors. Energy 2015, 90, 680–690. [Google Scholar] [CrossRef]
- Su, J.; Chen, Y.; Han, Z.; Zhou, D.; Bao, Y.; Zhao, Y. Investigation of V-Shaped Blade for the Performance Improvement of Vertical Axis Wind Turbines. Appl. Energy 2020, 260, 114326. [Google Scholar] [CrossRef]
- Narayan, G.; John, B. Effect of Winglets Induced Tip Vortex Structure on the Performance of Subsonic Wings. Aerosp. Sci. Technol. 2016, 58, 328–340. [Google Scholar] [CrossRef]
- Liu, C.; Gao, Y.; Tian, S.; Dong, X. Rortex—A New Vortex Vector Definition and Vorticity Tensor and Vector Decompositions. Phys. Fluids 2018, 30, 035103. [Google Scholar] [CrossRef]
- Spentzos, A.; Barakos, G.N.; Badcock, K.J.; Richards, B.E.; Coton, F.N.; Galbraith, R.A. McD.; Berton, E.; Favier, D. Computational Fluid Dynamics Study of Three-Dimensional Dynamic Stall of Various Planform Shapes. J. Aircr. 2007, 44, 1118–1128. [Google Scholar] [CrossRef]
- Xu, W.; Li, G.; Wang, F.; Li, Y. High-Resolution Numerical Investigation into the Effects of Winglet on the Aerodynamic Performance for a Three-Dimensional Vertical Axis Wind Turbine. Energy Convers. Manag. 2020, 205, 112333. [Google Scholar] [CrossRef]
Parameter | Value |
---|---|
Chord | 0.4 m |
Turbine Height | 3 m |
Turbine Diameter | 2.5 m |
Airfoil | NACA0015 |
Number of Blades | 3 |
Item | Description |
---|---|
Turbulence modeling | SST-RANS for steady and SST-IDDES for unsteady |
Discretization method | Cell-centered finite volume method |
Discretization order | Second-order by Barth’s interpolation |
Gradient computing method | Green–Gauss method |
Convective flux scheme | Roe scheme with the low-Mach preconditioning |
Viscous flux scheme | Central scheme |
Time-advancing scheme | Full implicit dual-time scheme |
Linear system solving method | Lower-Upper Symmetric Gauss-Seidel (LU-SGS) |
Turbulence modeling | SST-RANS for steady and SST-IDDES for unsteady |
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Zhang, T.; Wang, G.; Li, Q. Effects of a J-Shaped Blade on the Performance of a Vertical-Axis Wind Turbine Using the Improved Delayed Detached Eddy Simulation Method. Machines 2025, 13, 403. https://doi.org/10.3390/machines13050403
Zhang T, Wang G, Li Q. Effects of a J-Shaped Blade on the Performance of a Vertical-Axis Wind Turbine Using the Improved Delayed Detached Eddy Simulation Method. Machines. 2025; 13(5):403. https://doi.org/10.3390/machines13050403
Chicago/Turabian StyleZhang, Tengyue, Gang Wang, and Quanzheng Li. 2025. "Effects of a J-Shaped Blade on the Performance of a Vertical-Axis Wind Turbine Using the Improved Delayed Detached Eddy Simulation Method" Machines 13, no. 5: 403. https://doi.org/10.3390/machines13050403
APA StyleZhang, T., Wang, G., & Li, Q. (2025). Effects of a J-Shaped Blade on the Performance of a Vertical-Axis Wind Turbine Using the Improved Delayed Detached Eddy Simulation Method. Machines, 13(5), 403. https://doi.org/10.3390/machines13050403