Skip to main content
SpringerLink
Log in

Numerical simulations of a vertical-axis hydrokinetic turbine with different blade-strut configurations under free-surface effects

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

A numerical study of the free-surface flow over a vertical-axis hydrokinetic turbine with different blade-strut configurations is presented in this paper. The set of equations governing this multi-fluid flow consists of the Navier–Stokes equations and an advection equation of the signed distance function which describes the motion of the air–water interface in the context of the level-set method. For this application which involves domain motion, we adopt an arbitrary Lagrangian–Eulerian (ALE) description of the continuum where domain motion occurs independently of the fluid flow. Moreover, the variational multiscale (VMS) method is used for turbulence modelling resulting in the so-called ALE-VMS formulation. The formulation is used to investigate the performance of the turbine in four different computational settings. First, the quarter-struts and tip-struts configurations are simulated under a deep immersion depth. The results of the deep immersion cases show negligible effect from the free surface on the turbine performance. Next, the quarter-struts and tip-struts configurations are simulated under a shallow immersion depth. The results show significant effects of the turbine wake on the deformation of the air–water interface. A reduction in the performance of the turbine is observed in the shallow immersion cases and discussed. The results show robustness of the numerical formulation and provide opportunities for future studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Rogelj J, Elzen M, Hohne N, Fransen T, Fekete H, Winkler H, Schaeffer R, Sha F, Riahi K, Meinshausen M (2016) Paris agreement climate proposals need a boost to keep warming well below 2\(^\circ {\rm C}\). Perspective 534:631–639

    Google Scholar 

  2. Teske S (2019) Achieving the Paris climate agreement goals: global and regional 100% renewable energy scenarios with non-energy GHG pathways for +1.5\(^\circ\)C and +2\(^\circ\)C. Springer, Berlin

    Google Scholar 

  3. Pelc R, Fujit RM (2002) Renewable energy from the ocean. Mar Policy 26:471–479

    Google Scholar 

  4. Widén J, Carpman N, Castellucci V, Lingfor D, Olauson J, Remouit F, Bergkvist M, Grabbe M, Waters RJ (2015) Variability assessment and forecasting of renewables: a review for solar, wind, wave and tidal resources. Renew Sustain Energy Rev 44:356–375

    Google Scholar 

  5. Melikoglu M (2018) Current status and future of ocean energy sources: A global review. Ocean Eng 148:563–573

    Google Scholar 

  6. Laws N, Epps B (2016) Hydrokinetic energy conversion: technology, research, and outlook. Renew Sustain Energy Rev 57:1245–1259

    Google Scholar 

  7. Nachtane M, Tarfaoui M, Goda I, Rouway M (2020) A review on the technologies, design considerations and numerical models of tidal current turbines. Renew Energy 157:1274–1288

    Google Scholar 

  8. Dabiri J (2011) Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays. J Renew Sustain Energy 3. pp 043104--043117

  9. Brownstein I, Kinzel M, Dabiri J (2016) Performance enhancement of downstream vertical-axis wind turbines. J Renew Sustain Energy 8. pp 053306--053325

  10. Hezaveh S, Bou-Zeid E, Dabiri J, Kinzel M, Cortina G, Martinelli L (2018) Increasing the power production of vertical-axis wind-turbine farms using synergistic clustering. Bound-Layer Meteorol 169:275–296

    Google Scholar 

  11. Brownstein I, Wei N, Dabiri J (2019) Aerodynamically interacting vertical-axis wind turbines: performance enhancement and three-dimensional flow. Energies 12. pp 2724--2747

  12. Katopodes N (2018) Free-surface flow: computational methods. Elsevier, Amsterdam

    Google Scholar 

  13. Elgeti S, Sauerland H (2014) Deforming fluid domains within the finite element method: Five mesh-based tracking methods in comparison. Arch Comput Methods Eng. 23:323--361

  14. Tezduyar T, Aliabadi S, Behr M (1998) Enhanced-Discretization Interface-Capturing Technique (EDICT) for computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 155:235–248

    MATH  Google Scholar 

  15. Bayram Mohamed A, Abdulrahman M, Guaily A (2022) Simplified level set method coupled to stabilised finite element flow solver for moving boundaries. Progress Comput Fluid Dyn Int J 22(1):1–14. https://doi.org/10.1504/PCFD.2022.120265

    Article  MathSciNet  Google Scholar 

  16. Whelan J, Thomson M, Graham1and J, Peiro J (2007) Modelling of free surface proximity and wave induced velocities around a horizontal axis tidal stream turbine. In: Proceedings of the 7th European Wave and Tidal Energy Conference. 7:35

  17. Consul C, Willden R, McIntosh S (2013) Blockage effects on the hydrodynamic performance of a marine cross-flow turbine. Philos Trans R Soc A Math Phys Eng Sci 371. pp 20120299--20120315

  18. Bahaj A, Molland A, Chaplin J, Batten W (2007) Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank. Renew Energy 32:407–426

    Google Scholar 

  19. Bai X, Avital E, Munjiza A, Williams J (2014) Numerical simulation of a marine current turbine in free surface flow. Renew Energy 63:715–723

    Google Scholar 

  20. Riglin J, Schleicher W, Liu I, Oztekin A (2015) Characterization of a micro-hydrokinetic turbine in close proximity to the free surface. Ocean Eng 110:270–280

    Google Scholar 

  21. Hocine A, Lacey R, Poncet S (2019) Multiphase modeling of the free surface flow through a Darrieus horizontal axis shallow-water turbine. Renew Energy 143:1890–1901

    Google Scholar 

  22. Kolekar N, Banerjee A (2015) Performance characterization and placement of a marine hydrokinetic turbine in a tidal channel under boundary proximity and blockage effects. Appl Energy 148:121–133

    Google Scholar 

  23. Gosselin R, Dumas G, Boudreau M (2016) Parametric study of H-Darrieus vertical-axis turbines using CFD simulations. J Renew Sustain Energy 8. pp 053301--053324

  24. Rezaeiha A, Montazeri H, Blocken B (2018) Towards optimal aerodynamic design of vertical axis wind turbines: impact of solidity and number of blades. Energy 165:1129–1148

    Google Scholar 

  25. Guillaud N, Balarac G, Goncalvès E, Zanette J (2020) Large eddy simulations on vertical axis hydrokinetic turbines-power coefficient analysis for various solidities. Renew Energy 147:473–486

    Google Scholar 

  26. Nguyen M, Balduzzi F, Goude A (2021) Effect of pitch angle on power and hydrodynamics of a vertical axis turbine. Ocean Eng 238. pp 109335--109350

  27. Sun K, Yi Y, Zhang J, Zhang J, Zaidi S, Sun S (2022) Influence of blade numbers on start-up performance of vertical axis tidal current turbines. Ocean Eng 243. pp 110314—110322

  28. Marsh P, Ranmuthugala D, Penesis I, Thomas G (2015) Three-dimensional numerical simulations of straight-bladed vertical axis tidal turbines investigating power output, torque ripple and mounting forces. Renew Energy 83:67–77

    Google Scholar 

  29. Strom B, Johnson N, Polagye B (2018) Impact of blade mounting structures on cross-flow turbine performance. J Sustain Renew Energy 10. pp 034504--034522

  30. Villeneuve T, Winckelmans G, Dumas G (2021) Increasing the efficiency of vertical-axis turbines through improved blade support structures. Renew Energy 169:1386–1401

    Google Scholar 

  31. Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197(1–4):173–201

    MathSciNet  MATH  Google Scholar 

  32. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43(1):3–37

    MathSciNet  MATH  Google Scholar 

  33. Bayram AM, Bear C, Bear M, Korobenko A (2020) Performance analysis of two vertical-axis hydrokinetic turbines using variational multiscale method. Computers & Fluids 200:104432. https://doi.org/10.1016/j.compfluid.2020.104432 (Available online)

    Article  MathSciNet  MATH  Google Scholar 

  34. Dhalwala M, Bayram A, Oshkai P, Korobenko A (2022) Performance and near-wake analysis of a vertical-axis hydrokinetic turbine under a turbulent inflow. Ocean Eng 257:111703 (Available online)

    Google Scholar 

  35. Bayram A, Korobenko A (2020) Variational multiscale framework for cavitating flows. Comput Mech 66:49–67. https://doi.org/10.1007/s00466-020-01840-2

    Article  MathSciNet  MATH  Google Scholar 

  36. Bayram A, Korobenko A (2021) A numerical formulation for cavitating flows around marine propellers based on variational multiscale method. Comput Mech 68:405–432. https://doi.org/10.1007/s00466-021-02039-9

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhu Q, Yan J (2021) A moving-domain cfd solver in fenics with applications to tidal turbine simulations in turbulent flows. Comput Math Appl 81:532–546

    MathSciNet  MATH  Google Scholar 

  38. Yan J, Deng X, Korobenko A, Bazilevs Y (2017) Free-surface flow modeling and simulation of horizontal-axis tidal-stream turbines. Comput Fluids 158:157–166. https://doi.org/10.1016/j.compfluid.2016.06.016

    Article  MathSciNet  MATH  Google Scholar 

  39. Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2012) Free-surface flow and fluid-object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech 79:010905

    Google Scholar 

  40. Akkerman I, Dunaway J, Kvandal J, Spinks J, Bazilevs Y (2012) Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS. Comput Mech 50:719–727

    Google Scholar 

  41. Yan J, Korobenko A, Deng X, Bazilevs Y (2016) Computational free-surface fluid-structure interaction with application to floating offshore wind turbines. Comput Fluids 141:155–174

    MathSciNet  MATH  Google Scholar 

  42. Akkerman I (2017) Monotone level-sets on arbitrary meshes without redistancing. Comput Fluids 146:74–85

    MathSciNet  MATH  Google Scholar 

  43. Bazilevs Y, Yan J, Deng X, Korobenko A (2018) Computer modeling of wind turbines: 2. Free-surface FSI and fatigue-damage. Arch Comput Methods Eng 26:1101–1115

    MathSciNet  Google Scholar 

  44. Akkerman I, Eikelder M (2019) Toward free-surface flow simulations with correct energy evolution: an isogeometric level-set approach with monolithic time-integration. Comput Fluids 181:77–89

    MathSciNet  MATH  Google Scholar 

  45. Yan J, Deng X, Xu F, Xu S, Zhu Q (2020) Numerical simulations of two back-to-back horizontal axis tidal stream turbines in free-surface flows. J Appl Mech 87. pp 061001--061011

  46. Zhu Q, Xu F, Xu S, Hsu M-C, Yan J (2020) An immersogeometric formulation for free-surface flows with application to marine engineering problems. Comput Methods Appl Mech Eng 361. pp 112748--112772

  47. Osher S, Fedkiw R (2002) Level set methods and dynamic implicit surfaces. In: Applied mathematical sciences. Springer, New York (ISBN 9780387954820)

  48. Tezduyar TE, Sathe S (2003) Stabilization parameters in SUPG and PSPG formulations. J Comput Appl Mech 4(1):71–88

    MathSciNet  MATH  Google Scholar 

  49. Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput fluids 36(2):191–206

    MathSciNet  MATH  Google Scholar 

  50. Tezduyar TE, Ramakrishnan S, Sathe S (2008) Stabilized formulations for incompressible flows with thermal coupling. Int J Numer Methods Fluids 57(9):1189–1209

    MathSciNet  MATH  Google Scholar 

  51. Hsu M-C, Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput Methods Appl Mech Eng 199(13–16):828–840

    MathSciNet  MATH  Google Scholar 

  52. Takizawa K, Tezduyar TE, Otoguro Y (2018) Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations. Comput Mech 62:1169–1186. https://doi.org/10.1007/s00466-018-1557-x

    Article  MathSciNet  MATH  Google Scholar 

  53. Bazilevs Y, Hughes TJR (2007) Weak imposition of dirichlet boundary conditions in fluid mechanics. Comput Fluids 36(1):12–26

    MathSciNet  MATH  Google Scholar 

  54. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196(49–52):4853–4862

    MathSciNet  MATH  Google Scholar 

  55. Xu F, Moutsanidis G, Kamensky D, Hsu M-C, Murugan M, Ghoshal A, Bazilevs Y (2017) Compressible flows on moving domains: stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling. Comput Fluids 158:201–220

    MathSciNet  MATH  Google Scholar 

  56. Bazilevs Y, Takizawa K, Wu MCH, Kuraishi T, Avsar R, Xu Z, Tezduyar TE (2021) Gas turbine computational flow and structure analysis with isogeometric discretization and a complex-geometry mesh generation method. Comput Mech 67(1):57–84

    MathSciNet  MATH  Google Scholar 

  57. Cen H, Zhou Q, Korobenko A (2022) Wall-function-based weak imposition of Dirichlet boundary condition for stratified turbulent flows. Comput Fluids 234:105257

    MathSciNet  MATH  Google Scholar 

  58. Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43(5):555–575

    MathSciNet  MATH  Google Scholar 

  59. Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ\(\beta\) shock-capturing. Comput Fluids 36(1):147–159

    MATH  Google Scholar 

  60. Codoni D, Moutsanidis G, Hsu M-C, Bazilevs Y, Johansen C, Korobenko A (2021) Stabilized methods for high-speed compressible flows: toward hypersonic simulations. Comput Mech 67(3):785–809

    MathSciNet  MATH  Google Scholar 

  61. Codoni D, Johansen C, Korobenko A (2022) A streamline-upwind Petrov-Galerkin formulation for the analysis of hypersonic flows in thermal non-equilibrium. Comput Methods Appl Mech Eng 398:115185. https://doi.org/10.1016/j.cma.2022.115185 (ISSN 0045-7825)

    Article  MathSciNet  MATH  Google Scholar 

  62. Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230(11):4137–4152

    MathSciNet  MATH  Google Scholar 

  63. Löhner R, Yang C, Oñate E (2006) On the simulation of flows with violent free surface motion. Comput Methods Appl Mech Eng 195(41–43):5597–5620

    MathSciNet  MATH  Google Scholar 

  64. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha\) method. J Appl Mech

  65. Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha\) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 60(3–4):371-375

    MathSciNet  MATH  Google Scholar 

  66. Saad Y (2003) Iterative methods for sparse linear systems, vol 82. SIAM, Philadelphia

    MATH  Google Scholar 

  67. Gabriel E, Fagg GE, Bosilca G, Angskun T, Dongarra JJ, Squyres JM, Sahay V, Kambadur P, Barrett B, Lumsdaine A, Castain RH, Daniel DJ, Graham RL, Woodall TS (2004) Open MPI: Goals, concept, and design of a next generation MPI implementation. In: Proceedings. 11th European PVM/MPI Users’ Group Meeting. Budapest, Hungary, pp 97–104

  68. George K, Vipin K (2009) MeTis: unstructured graph partitioning and sparse matrix ordering system, Version 4.0. http://www.cs.umn.edu/~metis 11

  69. New Energy Corporation (2021) New Energy Corporation. https://www.newenergycorp.ca/ Accessed 17 Nov 2022

  70. Villeneuve T, Dumas G (2021) Impact of some design considerations on the wake recovery of vertical-axis turbines. Renew Energy 180:1419–1438

    Google Scholar 

  71. Bachant P, Wosnik M (2015) Characterising the near-wake of a cross-flow turbine. J Turbul 16:392–410

    Google Scholar 

Download references

Acknowledgements

We thank NSERC Alliance program and Alberta Innovates CASBE program for supporting the project. We thank Compute Canada and Advanced Research Computing at the University of Calgary for providing High Performance Computing resources that have contributed to the results in this paper.

Author information

Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada

    A. Bayram, M. Dhalwala & A. Korobenko

  2. Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 3P6, Canada

    P. Oshkai

Authors
  1. A. Bayram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Dhalwala
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Oshkai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Korobenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Korobenko.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bayram, A., Dhalwala, M., Oshkai, P. et al. Numerical simulations of a vertical-axis hydrokinetic turbine with different blade-strut configurations under free-surface effects. Engineering with Computers 39, 1041–1054 (2023). https://doi.org/10.1007/s00366-022-01758-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-022-01758-8

Keywords

Search

Navigation