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  • Featured in Physics
  • Open Access

Impact of Negative Geostrophic Wind Shear on Wind Farm Performance

Anja Stieren*, Jens H. Kasper, Srinidhi N. Gadde, and Richard J.A.M. Stevens†

  • Physics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, J. M. Burgers Center for Fluid Dynamics and MESA+ Research Institute, University of Twente, P. O. Box 217, Enschede 7500 AE, Netherlands

  • *a.stieren@utwente.nl
  • †r.j.a.m.stevens@utwente.nl
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PRX Energy 1, 023007 – Published 23 September, 2022

DOI: https://doi.org/10.1103/PRXEnergy.1.023007

Abstract

Baroclinicity, which leads to height-dependent driving pressure gradients, occurs in various situations such as the flow transition between land and sea, and sloping terrain. It has been shown that baroclinicity modifies the structure of the atmospheric boundary layer. For example, negative shear baroclinicity creates additional turbulence at higher elevations, which might influence the energy entrainment into large wind farms. Here, we use large-eddy simulations to study the effect of baroclinicity-induced negative shear on the wind farm power production and energy entrainment into a large wind farm. In agreement with the literature, our simulations show that negative geostrophic wind shear significantly modifies the mean wind velocity in the atmospheric boundary layer. Specifically, for the cases considered in the study, the negative geostrophic shear causes a change in the mean velocity up to 2.3 m/s at hub height, which greatly alters the wind farm power production. Additionally, we demonstrate with an energy budget analysis that a wind farm does not necessarily benefit from the additional turbulence created by the negative geostrophic wind shear. The reason for this is that the baroclinicity-induced negative shear alters the height and strength of the low-level jet and creates an upward flux above the jet, limiting the energy entrainment into the wind farm. Our results show that wind resources are altered in the boundary layer due to negative geostrophic wind shear and should be considered in wind farm modeling and power forecasts.

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synopsis

Wind Farms Perform Under Pressure

Published 23 September, 2022

Simulations show that negative wind shear can reduce the power output of wind farms.

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Using state-of-the-art simulations, the authors explore the effect of baroclinicity on wind farm performance. Such baroclinicity leads to height-dependent pressure gradients in the atmosphere. Typical wind farm models neglect baroclinic effects even though baroclinicity strongly influences atmospheric dynamics, for example, at flow transitions between land and sea. Consequently, baroclinicity influences the available wind resources and the performance of wind farms. In this study the authors focus on negative shear baroclinicity. They reveal that this type of baroclinicity can give rise to an upward turbulent flux above the wind farm, which reduces the overall energy entrainment into the farm. This contradicts the generally accepted view that atmospheric turbulence aids the energy entrainment into wind farms. Therefore, the authors argue that it is essential to account for atmospheric baroclinicity and incorporate its effects in wind farm design tools.

Article Text

References (91)

  1. R. J. A. M. Stevens and C. Meneveau, Flow structure and turbulence in wind farms, Annu. Rev. Fluid Mech. 49, 311 (2017).
  2. F. Porté-Agel, M. Bastankhah, and S. Shamsoddin, Wind-turbine and wind-farm flows: A review, Boundary-Layer Meteorol. 74, 1 (2020).
  3. A. K. Blackadar, Boundary layer wind maxima and their significance for the growth of nocturnal inversions, Bull. Am. Meteorol. Soc. 38, 283 (1957).
  4. J. W. Deardorff, Numerical investigation of neutral and unstable planetary boundary layers, J. Atmos. Sci. 29, 91 (1972).
  5. A. S. Monin and A. M. Obukhov, Basic laws of turbulent mixing in the surface layer of the atmosphere, Tr. Akad. Nauk SSSR Geophiz. Inst. 24, 163 (1954).
  6. S. K. Shah and E. Bou-Zeid, Direct numerical simulations of turbulent Ekman layers with increasing static stability: Modifications to the bulk structure and second-order statistics, J. Fluid Mech. 760, 494 (2014).
  7. J. R. Garratt, The atmospheric boundary layer, Earth-Sci. Rev. 37, 89 (1994).
  8. J. C. Kaimal and J. J. Finnigan, Atmospheric Boundary Layer Flows: Their Structure and Measurement (Oxford university press, Oxford, 1994).ISBN:9780195062397
  9. L. Mahrt, Stably stratified atmospheric boundary layers, Annu. Rev. Fluid Mech. 46, 23 (2014).
  10. D. Randall, S. Krueger, C. Bretherton, J. Curry, P. Duynkerke, M. Moncrieff, B. Ryan, D. Starr, M. Miller, W. Rossow, G. Tselioudis, and B. Wielicki, Confronting models with data: The GEWEX cloud systems study, Bull. Am. Meteorol. Soc. 84, 455 (2003).
  11. D. H. Lenschow, J. C. Wyngaard, and W. T. Pennell, Mean-field and second-moment budgets in a baroclinic, convective boundary layer, J. Atmos. Sci. 37, 1313 (1980).
  12. L. R. Hoxit, Planetary boundary layer winds in baroclinic conditions, J. Atmos. Sci. 31, 1003 (1974).
  13. S. P. S. Arya and J. C. Wyngaard, Effect of baroclinicity on wind profiles and the geostrophic drag law for the convective planetary boundary layer, J. Atmos. Sci. 32, 767 (1975).
  14. A. Smedman, Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer, Boundary-Layer Meteorol. 44, 231 (1988).
  15. A. R. Brown, Large-eddy simulation and parametrization of the baroclinic boundary-layer, Q. J. R. Meteorol. Soc. 122, 1779 (1996).
  16. A. R. Brown, Large-eddy simulation and parametrization of the effects of shear on shallow cumulus convection, Bound.-Layer Meteorol. 91, 65 (1999).
  17. R. M. Banta, R. K. Newsom, J. K. Lundquist, Y. L. Pichugina, R. L. Coulter, and L. Mahrt, Nocturnal low-level jet characteristics over Kansas during CASES-99, Boundary-Layer Meteorol. 105, 221 (2002).
  18. G. D. Hess, The neutral, barotropic planetary boundary layer, capped by a low-level inversion, Boundary-Layer Meteorol. 110, 319 (2004).
  19. W. D. Smyth and J. R. Carpenter, Instability in Geophysical Flows (Cambridge University Press, Cambridge, 2019), 195.
  20. L. Conangla and J. Cuxart, On the turbulence in the upper part of the low-level jet: An experimental and numerical study, Boundary-Layer Meteorol. 118, 379 (2006).
  21. V. W. Ekman, On the influence of the Earth’s rotation on ocean-currents, Arch. Math., Astron. Phys. 2, 1 (1905).
  22. R. Stoll, J. A. Gibbs, S. T. Salesky, W. Anderson, and M. Calaf, Large-eddy simulation of the atmospheric boundary layer, Bound.-Layer Meteorol. 177, 541 (2020).
  23. R. Floors, A. Peña, and S. E. Gryning, The effect of baroclinicity on the wind in the planetary boundary layer, Q. J. R. Meteorol. Soc. 141, 619 (2015).
  24. M. Momen, E. Bou-Zeid, M. B. Parlange, and M. Giometto, Modulation of mean wind and turbulence in the atmospheric boundary layer by baroclinicity, J. Atmos. Sci. 75, 3797 (2018).
  25. J. R. Holton, The diurnal boundary layer wind oscillation above sloping terrain, Tellus 19, 200 (1967).
  26. A.-S. Smedman, M. Tjernström, and U. Högström, Analysis of the turbulence structure of a marine low-level jet, Boundary-Layer Meteorol. 66, 105 (1993).
  27. M. Momen, Baroclinicity in stable atmospheric boundary layers: Characterizing turbulence structures and collapsing wind profiles via reduced models and large-eddy simulations, Q. J. R. Meteorol. 148, 76 (2022).
  28. S. S. Zilitinkevich and I. N. Esau, The effect of baroclinicity on the equilibrium depth of neutral and stable planetary boundary layers, Q. J. R. Meteorol. Soc. 129, 3339 (2003).
  29. S. S. Zilitinkevich and I. N. Esau, Resistance and heat-transfer laws for stable and neutral planetary boundary layers: Old theory advanced and re-evaluated, Q. J. R. Meteorol. Soc. 131, 1863 (2005).
  30. S. Basu, J. Vinuesa, and A. Swift, Dynamic LES modeling of a diurnal cycle, J. Appl. Meteorol. Climatoly 47, 1156 (2008).
  31. V. Kumar, G. Svensson, A. A. M. Holtslag, C. Meneveau, and M. B. Parlange, Impact of surface flux formulations and geostrophic forcing on large-eddy simulations of diurnal atmospheric boundary layer flow, J. Appl. Meteorol. Climatol. 49, 1496 (2010).
  32. J. G. Pedersen, M. Kelly, S. E. Gryning, and B. Brümmer, The effect of unsteady and baroclinic forcing on predicted wind profiles in large eddy simulations: Two case studies of the daytime atmospheric boundary layer, Meteorol. Z. 22, 661 (2013).
  33. Z. Sorbjan, Large-eddy simulations of the baroclinic mixed layer, Boundary-Layer Meteorol. 112, 57 (2004).
  34. K. Ghannam and E. Bou-Zeid, Baroclinicity and directional shear explain departures from the logarithmic wind profile, Q. J. R. Meteorol. Soc. 147, 443 (2021).
  35. A. Doosttalab, D. Siguenza-Alvarado, V. Pulletikurthi, Y. Jin, H. B. Evans, L. P. Chamorro, and L. Castillo, Interaction of low-level jets with wind turbines: On the basic mechanisms for enhanced performance, J. Renew. Sustain. Energy 12, 053301 (2020).
  36. S. N. Gadde and R. J. A. M. Stevens, Effect of turbine-height on wind farm performance in the presence of a low-level jet, J. Renew. Sustain. Energy 13, 013305 (2021).
  37. J. A. Aird, R. J. Barthelmie, T. J. Shepherd, and S. C. Pryor, WRF-simulated low-level jets over Iowa: Characterization and sensitivity studies, Wind Energy Sci. 6, 1015 (2021).
  38. M. Calaf, C. Meneveau, and J. Meyers, Large eddy simulations of fully developed wind-turbine array boundary layers, Phys. Fluids 22, 015110 (2010).
  39. J. Meyers and C. Meneveau, Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms, J. Fluid Mech. 715, 335 (2013).
  40. R. J. A. M. Stevens, Dependence of optimal wind-turbine spacing on wind-farm length, Wind Energy 19, 651 (2016).
  41. Y.-T. Wu and F. Porté-Agel, Modeling turbine wakes and power losses within a wind farm using LES: An application to the Horns Rev offshore wind farm, Renewable Energy 75, 945 (2015).
  42. J. P. Goit and J. Meyers, Optimal control of energy extraction in wind-farm boundary layers, J. Fluid Mech. 768, 5 (2015).
  43. M. Zhang, M. G. Arendshorst, and R. J. A. M. Stevens, Large eddy simulations of the effect of vertical staggering in extended wind farms, Wind Energy 22, 189 (2019).
  44. G. Cortina, V. Sharma, R. Torres, and M. Calaf, Mean kinetic energy distribution in finite-size wind farms: A function of turbines’ arrangement, Renew. Energy 148, 585 (2020).
  45. H. Lu and F. Porté-Agel, Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer, Phys. Fluids 23, 065101 (2011).
  46. M. Calaf, M. B. Parlange, and C. Meneveau, Large eddy simulation study of scalar transport in fully developed wind-turbine array boundary layers, Phys. Fluids 23, 126603 (2011).
  47. M. Dörenkämper, B. Witha, G. Steinfeld, D. Heinemann, and M. Kühn, The impact of stable atmospheric boundary layers on wind-turbine wakes within offshore wind farms, J. Wind Eng. Ind. Aerodyn. 144, 146 (2015).
  48. M. Abkar and F. Porté-Agel, Influence of atmospheric stability on wind-turbine wakes: A large-eddy simulation study, Phys. Fluids 27, 035104 (2015).
  49. D. Allaerts and J. Meyers, Large eddy simulation of a large wind-turbine array in a conventionally neutral atmospheric boundary layer, Phys. Fluids 27, 065108 (2015).
  50. K. L. Wu and F. Porté-Agel, Flow adjustment inside and around large finite-size wind farms, Energies 10, 2164 (2017).
  51. J. S. Na, E. Koo, E. K. Jin, R. Linn, S. C. Ko, D. Muñoz-Esparza, and J. S. Lee, Large-eddy simulations of wind-farm wake characteristics associated with a low-level jet, Wind Energy 21, 163 (2018).
  52. N. Ali, N. Hamilton, M. Calaf, and R. B. Cal, Turbulence kinetic energy budget and conditional sampling of momentum, scalar, and intermittency fluxes in thermally stratified wind farms, J. Turbul. 20, 32 (2019).
  53. O. Maas and S. Raasch, Wake properties and power output of very large wind farms for different meteorological conditions and turbine spacings: A large-eddy simulation case study for the German Bight, Wind Energy Sci. 7, 715 (2022).
  54. S. N. Gadde and R. J. A. M. Stevens, Effect of Coriolis force on a wind farm wake, J. Phys. Conf. Ser. 1256, 012026 (2019).
  55. M. F. Howland, A. S. Ghate, and S. K. Lele, Influence of the geostrophic wind direction on the atmospheric boundary layer flow, J. Fluid Mech. 883, A39 (2020).
  56. M. Abkar and F. Porté-Agel, Influence of the Coriolis force on the structure and evolution of wind turbine wakes, Phys. Rev. Fluids 1, 063701 (2016).
  57. P. Veers, et al., Grand challenges in the science of wind energy, Science 366, eaau2027 (2019).
  58. D. Allaerts, E. Quon, C. Draxl, and M. Churchfield, Development of a time–height profile assimilation technique for large-eddy simulation, Boundary-Layer Meteorol. 176, 329 (2020).
  59. C. Draxl, D. Allaerts, E. Quon, and M. Churchfield, Coupling mesoscale budget components to large-eddy simulations for wind-energy applications, Boundary-Layer Meteorol. 179, 73 (2021).
  60. J. Sanz Rodrigo, M. Churchfield, and B. Kosović, A methodology for the design and testing of atmospheric boundary layer models for wind energy applications, Wind Energy Sci. 2, 35 (2017).
  61. J. Schalkwijk, H. J. J. Jonker, A. P. Siebesma, and F. C. Bosveld, A year-long large-eddy simulation of the weather over Cabauw: An overview, Mon. Weather Rev. 143, 828 (2015).
  62. J. D. Albertson and M. B. Parlange, Surface length-scales and shear stress: Implications for land-atmosphere interaction over complex terrain, Water Resour. Res. 35, 2121 (1999).
  63. S. N. Gadde, A. Stieren, and R. J. A. M. Stevens, Large-eddy simulations of stratified atmospheric boundary layers: Comparison of different subgrid models, Boundary-Layer Meteorol. 178, 363 (2021).
  64. S. N. Gadde and R. J. A. M. Stevens, Interaction between low-level jets and wind farms in a stable atmospheric boundary layer, Phys. Rev. Fluids 6, 014603 (2021).
  65. M. Abkar, H. J. Bae, and P. Moin, Minimum-dissipation scalar transport model for large-eddy simulation of turbulent flows, Phys. Rev. Fluids 1, 041701 (2016).
  66. J. B. Klemp and D. K. Lilly, Numerical simulation of hydrostatic mountain waves, J. Atmos. Sci. 35, 78 (1978).
  67. E. Bou-Zeid, C. Meneveau, and M. B. Parlange, A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows, Phys. Fluids 17, 025105 (2005).
  68. W. Brutsaert, Evaporation Into the Atmosphere: Theory, History and Applications Vol. 1 (Springer Science & Business Media, Dordrecht, 1982).
  69. R. J. Beare, M. K. Macvean, A. A. M. Holtslag, J. Cuxart, I. Esau, J.-C. Golaz, M. A. Jimenez, M. Khairoutdinov, B. Kosović, D. Lewellen, T. S. Lund, J. K. Lundquist, A. Mccabe, A. F. Moene, Y. Noh, S. Raasch, and P. Sullivan, An intercomparison of large eddy simulations of the stable boundary layer, Boundary-Layer Meteorol. 118, 247 (2006).
  70. R. J. A. M. Stevens, J. Graham, and C. Meneveau, A concurrent precursor inflow method for large eddy simulations and applications to finite length wind farms, Renewable Energy 68, 46 (2014).
  71. A. Stieren, S. N. Gadde, and R. J. A. M. Stevens, Modeling dynamic wind direction changes in large eddy simulations of wind farms, Renewable Energy 170, 1342 (2021).
  72. A. Sescu and C. Meneveau, A control algorithm for statistically stationary large-eddy simulations of thermally stratified boundary layers, Q. J. R. Meteorol. Soc. 140, 2017 (2014).
  73. J. N. Sørensen and W. Z. Shen, Numerical modeling of wind turbine wakes, J. Fluids Eng. 124, 393 (2002).
  74. L. Liu, L. Franceschini, D. F. Oliveira, F. C. C. Galeazzo, B. S. Carmo, and R. J. A. M. Stevens, Evaluating the accuracy of the actuator line model against blade element momentum theory in uniform inflow, Wind Energy 25, 1046 (2022).
  75. L. A. Martínez-Tossas, M. J. Churchfield, and C. Meneveau, Large eddy simulation of wind turbine wakes: Detailed comparisons of two codes focusing on effects of numerics and subgrid modeling, J. Phys. Conf. Ser. 625, 012024 (2015).
  76. M. Golbazi and C. L. Archer, Methods to estimate surface roughness length for offshore wind energy, Adv. Meteorol. 2019, 5695481 (2019).
  77. B. Kosović and J. A. Curry, A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer, J. Atmos. Sci. 57, 1052 (2000).
  78. J. Jonkman, S. Butterfield, W. Musial, and G. Scott, Definition of a 5-MW Reference Wind Turbine for Offshore System Development (National Renewable Energy Laboratory, Golden, Colorado, 2009).
  79. S. Gadde, L. Liu, and R. Stevens, Effect of low-level jet on turbine aerodynamic blade loading using large-eddy simulations, J. Phys. Conf. Ser. 1934, 012001 (2021).
  80. M. P. van der Laan and N. N. Sørensen, Why the Coriolis force turns a wind farm wake clockwise in the northern hemisphere, Wind Energy Sci. 2, 285 (2017).
  81. D. Allaerts and J. Meyers, Boundary-layer development and gravity waves in conventionally neutral wind farms, J. Fluid Mech. 814, 95 (2017).
  82. M. Abkar and F. Porté-Agel, Mean and turbulent kinetic energy budgets inside and above very large wind farms under conventionally-neutral condition, Renewable Energy 70, 142 (2014).
  83. G. Cortina, M. Calaf, and R. B. Cal, Distribution of mean kinetic energy around an isolated wind turbine and a characteristic wind turbine of a very large wind farm, Phys. Rev. Fluids 1, 074402 (2016).
  84. C. VerHulst and C. Meneveau, Large eddy simulation study of the kinetic energy entrainment by energetic turbulent flow structures in large wind farms, Phys. Fluids 26, 025113 (2014).
  85. R. B. Cal, J. Lebrón, L. Castillo, H. S. Kang, and C. Meneveau, Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer, J. Renew. Sustain. Energy 2, 013106 (2010).
  86. N. Hamilton, H. S. Kang, C. Meneveau, and R. B. Cal, Statistical analysis of kinetic energy entrainment in a model wind turbine array boundary layer, J. Renew. Sustain. Energy 4, 063105 (2012).
  87. H. Lu and F. Porté-Agel, On the impact of wind farms on a convective atmospheric boundary layer, Bound.-Layer Meteorol. 157, 81 (2015).
  88. D. Yang, C. Meneveau, and L. Shen, Large-eddy simulation of offshore wind farm, Phys. Fluids 26, 025101 (2014).
  89. M. Abkar and F. Porté-Agel, The effect of free-atmosphere stratification on boundary-layer flow and power output from very large wind farms, Energies 6, 2338 (2013).
  90. W. Munters, C. Meneveau, and J. Meyers, Turbulent inflow precursor method with time-varying direction for large-eddy simulations and applications to wind farms, Boundary-Layer Meteorol. 159, 305 (2016).
  91. I. Sood, E. Simon, A. Vitsas, B. Blockmans, G. C. Larsen, and J. Meyers, Comparison of Large Eddy Simulations against measurements from the Lillgrund offshore wind farm, Wind Energy Sci. 1 (2022).

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PRX Energy 1, 023007– Published 23 September, 2022
  • Received 27 April 2022
  • Revised 7 July 2022
  • Accepted 17 August 2022
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