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Numerical analysis of the performance of a three-bladed vertical-axis turbine with active pitch control using a coupled unsteady Reynolds-averaged Navier-Stokes and actuator line model

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Abstract

In this paper, we present a numerical model of a vertical-axis turbine (VAT) with active-pitch torque control. The model is based upon the Wind and Tidal Turbine Embedded Simulator (WATTES) and WATTES-V turbine realisations in conjunction with the actuator line method (ALM), and uses OpenFOAM to solve the unsteady Reynolds-averaged Navier-Stokes (URANS) equations with two-equation k - ε turbulence closure. Our novel pitch-controlled system is based on an even pressure drop across the entire rotor to mitigate against dynamic stall at low tip speed ratio. The numerical model is validated against experimental measurements and alternative numerical predictions of the hydrodynamic performance of a 1:6 scale UNH-RM2 hydrokinetic turbine. Simulations deploying the variable pitch mechanism exhibit improved turbine performance compared to measured data and fixed zero-pitch model predictions. Near-wake characteristics are investigated by examining the vorticity distribution near the turbine. The pitch-controlled system is demonstrated to theoretically decrease turbulence generated by turbine rotations, mitigate the intensity of vortex shedding and size of detached vortices, and significantly enhance the performance of a vertical-axis hydrokinetic turbine for rated tip-speed ratios.

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References

  1. Borthwick A. G. L. Marine renewable energy seascape [J]. Engineering, 2016, 2(1): 69–78.

    Article  Google Scholar 

  2. IEA. Energy and climate change [R]. World Energy Outlook Special Report, 2015.

  3. Mathew S. Wind energy: Fundamentals, resource analysis and economics [M]. Berlin, Germany: Springer, 2007.

    Google Scholar 

  4. Rezaeiha A., Kalkman I., Blocken B. Effect of pitch angle on power performance and aerodynamics of a vertical axis wind turbine [J]. Applied Energy, 2017, 197: 132–150.

    Article  Google Scholar 

  5. Salter S. H. Are nearly all tidal stream turbine designs wrong? [C]. 4th International Conference on Ocean Energy, Edinburgh, UK, 2012.

  6. Aslam Bhutta M. M., Hayat N., Farooq A. U. et al. Vertical axis wind turbine–A review of various configurations and design techniques [J]. Renewable and Sustainable Energy Reviews, 2012, 16(4): 1926–1939.

    Article  Google Scholar 

  7. Salter S. H., Taylor J. R. M. Vertical-axis tidal-current generators and the Pentland Firth [J]. Proceedings of the Institution of Mechanical Engeers, Part A: J. Power Energy, 2007, 221(2): 181–199.

    Article  Google Scholar 

  8. Sutherland H. J., Berg D. E., Ashwill T. D. A retrospective of VAWT technology [R]. Technical Report SAND2012-0304, Sandia National Laboratories, 2012.

  9. Sahim K., Santoso D., Puspitasari D. Investigations on the effect of radius rotor in combined darrieus-savonius wind turbine [J]. International Journal of Rotating Machinery, 2018, 3568542.

  10. Subramanian A., Yogesh S. A., Sivanandan H. et al. Effect of airfoil and solidity on performance of small scale vertical axis wind turbine using three dimensional CFD model [J]. Energy, 2017, 133: 179–190.

    Article  Google Scholar 

  11. Dyachuk E. Aerodynamics of vertical axis wind turbines–Development of simulation tools and experiments [D]. Doctoral Thesis, Uppsala, Sweden: Uppsala University, 2015.

    Google Scholar 

  12. Li Y., Calisal S. M. Three-dimensional effects and arm effects on modeling a vertical axis tidal current turbine [J]. Renewable Energy, 2010, 35(10): 2325–2334.

    Article  Google Scholar 

  13. Li Y., Calisal S. M. Modeling of twin-turbine systems with vertical axis tidal current turbine: Part II torque fluctuation [J]. Ocean Engineering, 2011, 38(4): 550–558.

    Article  Google Scholar 

  14. Buntine J. D., Pullin D. I. Merger and cancellation of strained vortices [J]. Journal of Fluid Mechanics, 1989, 206: 263–295.

    Article  MATH  Google Scholar 

  15. McLaren K. W. A numerical and experimental study of unsteady loading of high solidity vertical axis wind turbines [D]. Doctoral Thesis, Hamilton, Canada: McMaster University, 2011.

    Google Scholar 

  16. Nobile R., Vahdati M., Barlow J. F. Unsteady flow simulation of a vertical axis wind turbine: A two-dimensional study [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2014, 125: 168–179.

    Article  Google Scholar 

  17. Biadgo A. M., Simonovic A., Komarov D. et al. Numerical and analytical investigation of vertical axis wind turbine [R]. Published Report, Belgrade, Serbia: Faculty of Engineering, 2013.

    Google Scholar 

  18. Bachant P., Wosnik M. UNH-RVAT Reynolds number dependence experiment: Reduced dataset and processing code [EB/OL]. URL: https://doi.org/10.6084/m9.figshare.1286960, 2016.

  19. Deardorff J. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers [J]. Journal of Fluid Mechanics, 1970, 41(2): 453–480.

    Article  MATH  Google Scholar 

  20. Smagorinsky J. General circulation experiments with the primitive equations [J]. Monthly Weather Review, 1963, 91(3): 99–164.

    Article  Google Scholar 

  21. Bianchini A., Balduzzi F., Bachant P. et al. Effectiveness of two-dimensional CFD simulations for Darrieus VAWTs: A combined numerical and experimental assessment [J]. Energy Conversion and Management, 2017, 136: 318–328.

    Article  Google Scholar 

  22. Melani P. F., Balduzzi F., Ferrara G. et al. Development of a desmodromic variable pitch system for hydrokinetic turbines [J]. Energy Conversion and Management, 2021, 250: 114890.

    Article  Google Scholar 

  23. Bachant P., Wosnik M. Effects of reynolds number on the energy conversion and near-wake dynamics of a high solidity vertical-axis cross-flow turbine [J]. Energies, 2016, 9(2): 73.

    Article  Google Scholar 

  24. Krogstad P. A., Eriksen P. E. “Blind test” calculations of the performance and wake development for a model wind turbine [J]. Renewable Energy, 2013, 50: 325–333.

    Article  Google Scholar 

  25. Hwang I. S., Lee Y. H., Kim S. J. Optimization of cycloidal water turbine and the performance improvement by individual blade control [J]. Applied Energy, 2009, 86(9): 1532–1540.

    Article  Google Scholar 

  26. Jing F., Sheng Q., Zhang L. Experimental research on tidal current vertical axis turbine with variable-pitch blades [J]. Ocean Engineering, 2014, 88: 228–241.

    Article  Google Scholar 

  27. Liang Y. B., Zhang L. X. et al. Blade pitch control of straight-bladed vertical axis wind turbine [J]. Journal of Central South University, 2016, 23(5): 1106–1114.

    Article  Google Scholar 

  28. Strom B., Brunton S. L., Polagye B. Intracycle angular velocity control of cross-flow turbines [J]. Natural Energy, 2017, 2: 17103.

    Article  Google Scholar 

  29. Dave M., Strom B., Snortland A. et al. Simulations of intracycle angular velocity control for a crossflow turbine [J]. American Institute of Aeronautics and Astronautics Journal, 2021, 59: 812–824.

    Article  Google Scholar 

  30. Kumar V. Repetitive control for floating offshore vertical axis wind turbine [D]. Master Thesis, Delft, The Netherlands: Delft University of Technology, 2017.

    Google Scholar 

  31. Kumar V., Savenije F. J., van Wingerden J. W. Repetitive pitch control for vertical axis wind turbine [J]. Journal of Physics: Conference Series, 2018, 1037, 032030.

    Google Scholar 

  32. Sagharichi A., Zamani M., Ghasemi A. Effect of solidity on the performance of variable-pitch vertical axis wind turbine [J]. Energy, 2018, 161: 753–775.

    Article  Google Scholar 

  33. Li C., Xiao Y., Xu Y. L. et al. Optimization of blade pitch in H-rotor vertical axis wind turbines through computational fluid dynamics simulations [J]. Applied Energy, 2018, 212: 1107–1125.

    Article  Google Scholar 

  34. Guo J., Zeng P., Lei L. Performance of a straight-bladed vertical axis wind turbine with inclined pitch axes by wind tunnel experiments [J]. Energy, 2019, 174: 553–561.

    Article  Google Scholar 

  35. Xu Y. L., Peng Y. X., Zhan S. Optimal blade pitch function and control device for high-solidity straight-bladed vertical axis wind turbines [J]. Applied Energy, 2019, 242: 1613–1625.

    Article  Google Scholar 

  36. Melani P. F., Balduzzi F., Ferrara G. et al. Tailoring the actuator line theory to the simulation of vertical-axis wind turbines [J]. Energy Conversion and Management, 2021, 243: 114422.

    Article  Google Scholar 

  37. Lang C. Harnessing tidal energy takes new turn: could the application of the windmill principle produce a sea change? [J]. IEEE Spectrum, 2003, 40(9): 13.

    Article  Google Scholar 

  38. Khan M. J., Bhuyan G., Iqbal M. T. et al. Hydrokinetic energy conversion systems and assessment of horizontal and vertical axis turbines for river and tidal applications: A technology status review [J]. Applied Energy, 2009, 86: 1823–1835.

    Article  Google Scholar 

  39. Zhao R., Creech A. C. W., Borthwick A. G. L. et al. Aerodynamic analysis of a two-bladed vertical-axis wind turbine using a coupled unsteady RANS and actuator line model [J]. Energies, 2020, 13(4): 776.

    Article  Google Scholar 

  40. Salter S. Consultation on Scotland’s Energy Efficiency Program: Tidal Stream Energy from the Pentland Firth [R]. 2018.

  41. Houf D. P. Active pitch control of a vertical axis wind turbine [D]. Master Thesis, Delft, The Netherlands: Delft University of Technology, 2016.

    Google Scholar 

  42. Bachant P., Goude A., Wosnik M. Actuator line modeling of vertical-axis turbines [R]. Non-peer-reviewed article, 2018, arXiv:1605.01449.

  43. Creech A. C. W., Früh W. G., Maguire A. E. Simulations of an offshore wind farm using large-eddy simulation and a torque-controlled actuator disc model [J]. Surveys in Geophysics, 2015, 36: 427–481.

    Article  Google Scholar 

  44. Creech A. C. W., Früh W. G. Modeling wind turbine wakes for wind farms (Alternative energy and shale gas encyclopedia) [M]. New York, USA: John Wiley and Sons, 2016.

    Google Scholar 

  45. Creech A. C. W., Borthwick A. G. L., Ingram D. Effects of support structures in an LES actuator line model of a tidal turbine with contra-rotating rotors [J]. Energies, 2017, 10(5): 726.

    Article  Google Scholar 

  46. Zhao R., Creech A. C. W., Borthwick A. G. L. et al. Coupling of WATTES and OpenFOAM codes for wake modelling behind close-packed contra-rotating vertical-axis tidal rotors [C]. Proceedings of the 6th Oxford Tidal Energy Workshop, Oxford, UK, 2018.

  47. Salter S. H. Private communication [R]. 2019.

  48. Barone M., Griffith T., Berg J. Reference model 2: “Rev 0” rotor design [R]. Technical Report SAN2011-9306, Sandia National Laboratories, 2011.

  49. Bachant P., Wosnik M. Reynolds number dependence of cross-flow turbine performance and near-wake characteristics [C]. Proceedings of the 2nd Marine Energy Technology Symposium, Seattle, USA, 2014.

  50. Bachant P., Wosnik M., Gunawan B. et al. Experimental study of a reference model vertical-axis cross-flow turbine [J]. PLOS ONE, 2016, 11(9): e0163799.

    Article  Google Scholar 

  51. Bachant P., Wosnik M. Performance and near-wake measurements for a vertical axis turbine at moderate Reynolds number [C]. American Society of Mechanical Engineers: Fluids Engineering Division Summer Meeting, Incline Village, Nevada, USA, 2013.

  52. Bachant P., Wosnik M. Modeling the near-wake of a vertical-axis cross-flow turbine with 2-D and 3-D RANS [J]. Journal of Renewable and Sustainable Energy, 2016, 8(5): 053311.

    Article  Google Scholar 

  53. Wosnik M., Bachant P., Gunawan B. et al. Performance measurements for a 1:6 scale model of the doe reference model 2 (Rm2) cross-flow hydrokinetic turbine [C]. Proceedings of the 3rd Marine Energy Technology Symposium, Washington DC, USA, 2015.

  54. Roache P. J. Perspective: A method for uniform reporting of grid refinement studies [J]. Journal of Fluids Engineering, 1994, 116(3): 405–413.

    Article  Google Scholar 

  55. de Moura C. A., Kubrusly C. S. The Courant-Friedrichs-Lewy (CFL) condition: 80 Years after its discovery [M]. Boston, USA: Birkhauser, 2013.

    Book  MATH  Google Scholar 

  56. Wosnik M., Bachant P., Neary V. S. et al. Evaluation of design and analysis code, CACTUS, for predicting cross-flow hydrokinetic turbine performance [R]. Sandia National Laboratories Report, 2016.

  57. Creech A. C. W. A three-dimensional numerical model of a horizontal axis, energy extracting turbine [D]. Doctoral Thesis, Edinburgh, UK: Heriot-Watt University, 2009.

    Google Scholar 

  58. Zhao R., Creech A. C. W., Borthwick A. G. L. et al. Numerical model of a vertical-axis cross-flow tidal turbine [C]. ASME 39th International Conference on Ocean, Offshore and Arctic Engineering, 2020, Virtual Online.

  59. Bianchini A., Balduzzi F., Banchant P. et al. Effectiveness of two-dimensional CFD simulations for Darrieus VAWTs: A combined numerical and experimental assessment [J]. Energy Conversion and Management. 2017, 136: 318–328.

    Article  Google Scholar 

  60. Bianchini A., Carnevale E., Ferrari L. A model to account for the virtual camber effect in the performance prediction of an H-darrieus VAWT using the momentum models [J]. Wind Engineering, 2011, 35: 465–482.

    Article  Google Scholar 

  61. Yang Y., Guo Z., Song Q. et al. Effect of blade pitch angle on the aerodynamic characteristics of a straight-bladed vertical axis wind turbine based on experiments and simulations [J]. Energies, 2018, 11(6): 1514.

    Article  Google Scholar 

  62. Sheldahl R. E., Klimas P. C. Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical axis wind turbines [R]. Sandia National Laboratories Energy Report, 1981.

  63. Chen B., Su S., Viola I. M. et al. Numerical investigation of vertical-axis tidal turbines with sinusoidal pitching blades [J]. Ocean Engineering, 2018, 155: 75–87.

    Article  Google Scholar 

  64. Melani P. F., Balduzzi F., Ferrara G. et al. An annotated database of low Reynolds aerodynamic coefficients for the NACA0018 airfoil [C]. AIP Conference Proceedings, 2019, 2191: 020110.

    Article  Google Scholar 

  65. Xu W., Li G., Zheng X. et al. High-resolution numerical simulation of the performance of vertical axis wind turbines in urban area: Part I, Wind turbines on the side of single building [J]. Renewable Energy, 2021, 177: 461–474.

    Article  Google Scholar 

  66. Li Q., Maeda T., Kamada Y. et al. The influence of flow field and aerodynamic forces on a straight-bladed vertical axis wind turbine [J]. Energy, 2016, 111: 260–271.

    Article  Google Scholar 

  67. Li Y., Calişal S. M. Modeling of twin-turbine systems with vertical axis tidal current turbines: Part I–Power output [J]. Ocean Engineering, 2010, 37: 627–637.

    Article  Google Scholar 

  68. Sagharichi A., Maghrebi M. J., Arabgolarcheh A. Variable pitch blades: An approach for improving performance of Darrieus wind turbine [J]. Journal of Renewable Sustainable Energy, 2016, 8(5): 053305.

    Article  Google Scholar 

  69. Araya D. B., Dabiri J. O. A comparison of wake measurements in motor-driven and flow-driven turbine experiments [J]. Experiments in Fluids, 2015, 56: 150.

    Article  Google Scholar 

  70. Brochier G., Fraunie P., Beguier C. et al. Water channel experiments of dynamic stall on Darrieus wind turbine blades [J]. Journal of Propulsion and Power, 1986, 2(5): 445–449.

    Article  Google Scholar 

  71. Ouro P., Stoesser T. An immersed boundary-based large-eddy simulation approach to predict the performance of vertical axis tidal turbines [J]. Computers and Fluids, 2017, 152: 74–87.

    Article  MathSciNet  MATH  Google Scholar 

  72. Réthoré P. E. Wind turbine wake in atmospheric turbulence [D]. Doctoral Thesis, Roskilde, Denmark: Technical University of Denmark, 2009.

    Google Scholar 

  73. El Kasmi A., Masson C. An extended k-ε model for turbulent flow through horizontal-axis wind turbines [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96: 103–122.

    Article  Google Scholar 

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Acknowledgments

The authors are grateful to Prof. Stephen Salter (The University of Edinburgh) for his pioneering contribution to the development of pitch-controlled vertical-axis turbines, and for his insightful suggestions that have informed the present research. The authors also deeply appreciate Dr. Takafumi Nishino (University of Oxford) for his guidance and expertise on fluid mechanics that have informed the present work.

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Authors and Affiliations

  1. Laboratory of Multi-function Towing Tank, State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 20024, China

    Rui-wen Zhao & Ye Li

  2. School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK

    Angus C. W. Creech

  3. School of Engineering, The University of Edinburgh, Edinburgh, UK

    Ye Li, Vengatesan Venugopal & Alistair G. L. Borthwick

  4. School of Engineering, Computing and Mathematics, University of Plymouth, Plymouth, UK

    Alistair G. L. Borthwick

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  1. Rui-wen Zhao
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  2. Angus C. W. Creech
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  3. Ye Li
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  4. Vengatesan Venugopal
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  5. Alistair G. L. Borthwick
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Corresponding author

Correspondence to Angus C. W. Creech.

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Conflict of interest: The authors declare that they have no conflict of interest. Ye Li, Alistair G. L. Borthwick are editorial board members for the Journal of Hydrodynamics and was not involved in the editorial review, or the decision to publish this article. All authors declare that there are no other competing interests.

Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent: Informed consent was obtained from all individual participants included in the study.

Additional information

Project supported by the Ministry of Science and Technology of China (Grant No. 2017YFE0132000), the National Natural Science Foundation of China (Grant No. 11872248).

Biography: Rui-wen Zhao (1991–), Female, Ph. D.

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Zhao, Rw., Creech, A.C.W., Li, Y. et al. Numerical analysis of the performance of a three-bladed vertical-axis turbine with active pitch control using a coupled unsteady Reynolds-averaged Navier-Stokes and actuator line model. J Hydrodyn 35, 516–532 (2023). https://doi.org/10.1007/s42241-023-0035-x

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