Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T08:16:41.991Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition

Published online by Cambridge University Press:  31 August 2017

N. Ali Open the ORCID record for N. Ali [Opens in a new window] ,
G. Cortina ,
N. Hamilton ,
M. Calaf  and
R. B. Cal
N. Ali
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, Portland, OR 97207, USA
G. Cortina
Affiliation:
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA
N. Hamilton
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, Portland, OR 97207, USA
M. Calaf
Affiliation:
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA
R. B. Cal*
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, Portland, OR 97207, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A large eddy simulation framework is used to explore the structure of the turbulent flow in a thermally stratified wind turbine array boundary layer. The flow field is driven by a constant geostrophic wind with time-varying surface boundary conditions obtained from a selected period of the CASES-99 field experiment. Proper orthogonal decomposition is used to extract coherent structures of the turbulent flow under the considered thermal stratification regimes. The flow structure is discussed in the context of three-dimensional representations of key modes, which demonstrate features ranging in size from the wind turbine wakes to the atmospheric boundary layer. Results demonstrate that structures related to the atmospheric boundary layer flow dominate over those introduced by the wind farm for the unstable and neutrally stratified regimes; large structures in atmospheric turbulence are beneficial for the wake recovery, and consequently the presence of the turbulent wind turbine wakes is diminished. Contrarily, the flow in the stably stratified case is fully dominated by the presence of the turbines and highly influenced by the Coriolis force. A comparative analysis of the test cases indicates that during the stable regime, higher-order modes contribute less to the overall character of the flow. Under neutral and unstable stratification, important turbulence dynamics are distributed over a larger range of basis functions. The influence of the wind turbines on the structure of the atmospheric boundary layer is mainly quantified via the turbulence kinetic energy of the first ten modes. Linking the new insights into structure of the wind turbine/atmospheric boundary layer and their interaction addressed here will benefit the formulation of new simplified models for commercial application.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Boundary Layers: Boundary layer structure Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 175 - 195
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abkar, M. & Porté-Agel, F. 2014 Mean and turbulent kinetic energy budgets inside and above very large wind farms under conventionally-neutral condition. Renewable Energy 70, 142–152.Google Scholar
Abkar, M., Sharifi, A. & Porté-Agel, F. 2016 Wake flow in a wind farm during a diurnal cycle. J. Turbul. 17 (4), 420–441.CrossRefGoogle Scholar
Albertson, J. D. & Parlange, M. B. 1999 Natural integration of scalar fluxes from complex terrain. Adv. Water Resour. 23 (3), 239–252.Google Scholar
Andersen, S., Sørensen, J. N. & Mikkelsen, R. 2013 Simulation of the inherent turbulence and wake interaction inside an infinitely long row of wind turbines. J. Turbul. 14 (4), 1–24.Google Scholar
Barthelmie, R. J. & Jensen, L. E. 2010 Evaluation of wind farm efficiency and wind turbine wakes at the Nysted offshore wind farm. Wind Energy 13, 573–586.Google Scholar
Bastine, D., Witha, B., Wächter, M. & Peinke, J. 2015 Towards a simplified dynamicwake model using pod analysis. Energies 8 (2), 895–920.CrossRefGoogle Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 1–18.Google Scholar
Brutsaert, W. 2005 Hydrology: An Introduction. Cambridge University Press.CrossRefGoogle Scholar
Brutsaert, W. & Parlange, M. B. 1992 The unstable surface layer above forest: regional evaporation and heat flux. Water Resources Research 28 (12), 3129–3134.CrossRefGoogle Scholar
Brutsaert, W., Parlange, M. B. & Gash, J. H. C. 1989 Neutral humidity profiles in the boundary layer and regional evaporation from sparse pine forest. Annales Geophysicae 7, 623–630.Google Scholar
Calaf, M., Parlange, M. B. & Meneveau, C. 2011 Large eddy simulation study of scalar transport in fully developed wind-turbine array boundary layers. Phys. Fluids 23, 126603.Google Scholar
Canuto, C., Hussainii, M. & Quarteroni, A. 1988 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Chamorro, L. & Porté-Agel, F. 2010 Effects of thermal stability and incoming boundary-layer flow characteristics on wind-turbine wakes: a wind-tunnel study. Boundary-Layer Meteorol. 136, 515–533.Google Scholar
Cortina, G., Cal, R. B. & Calaf, M. 2016 Distribution of mean kinetic energy around an isolated wind turbine and a characteristic wind turbine of a very large wind farm. Phys. Rev. Fluids 074402, 1–18.Google Scholar
Cortina, G. & Calaf, M. 2017 Turbulence upstream of wind turbines: a large-eddy simulation approach to investigate the use of wind lidars. Renewable Energy 105, 354–365.Google Scholar
Cortina, G., Sharma, V. & Calaf, M. 2017a Investigation of the incoming wind vector for improved wind turbine yaw-adjustment under different atmospheric and wind farm conditions. Renewable Energy 101, 376–386.Google Scholar
Cortina, G., Sharma, V. & Calaf, M. 2017b Wind farm density and harvested power in very large wind farms: a low-order model. Phys. Rev. Fluids 2, 074601.CrossRefGoogle Scholar
Fitch, A. C., Lundquist, J. K. & Olson, J. B. 2013 Mesoscale influences of wind farms throughout a diurnal cycle. Mon. Weath. Rev. 141, 2173–2198.Google Scholar
Garratt, J. R. 1994 Review: the atmospheric boundary layer. Earth-Science Reviews 37 (1–2), 89–134.Google Scholar
Hamilton, N., Tutkun, M. & Cal, R. B. 2015 Wind turbine boundary layer arrays for Cartesian and staggered configurations: part II, low-dimensional representations via the proper orthogonal decomposition. Wind Energy 18 (2), 297–315.Google Scholar
Hamilton, N., Tutkun, M. & Cal, R. B. 2016 Low-order representations of the canonical wind turbine array boundary layer via double proper orthogonal decomposition. Phys. Fluids 28 (2), 025103.Google Scholar
Hamilton, N., Tutkun, M. & Cal, R. B. 2017 Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition. Phys. Rev. Fluids 2 (1), 014601.Google Scholar
Hansen, K. S., Barthelmie, R. J., Jensen, L. E. & Sommer, A. 2012 The impact of turbulence intensity and atmospheric stability on power deficits due to wind turbine wakes at horns rev wind farm. Wind Energy 15 (1), 183–196.Google Scholar
Kumar, V., Svensson, G., Holtslag, A. M., Meneveau, C. & Parlange, M. B. 2010 Impact of surface flux formulations and geostrophic forcing on large-eddy simulations of diurnal atmospheric boundary layer flow. J. Appl. Meteorol. Climatol. 49, 1496–1516.Google Scholar
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation.Google Scholar
Mahrt, L. 1999 Stratified atmospheric boundary layers. Boundary-Layer Meteorol. 90 (3), 375–396.Google Scholar
Moeng, C.-H. 1984 A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41 (13), 2052–2062.Google Scholar
Monin, A. S. & Obukhov, A. M. 1954 Basic laws of turbulent mixing in the surface layer of the atmosphere. Tr. Akad. Nauk SSSR Geofiz. Inst. 24 (151), 163–187; English translation by John Miller, 1959.Google Scholar
Parlange, M. B. & Brustaert, W. 1993 Regional shear stress of broken forest from radiosonde wind profiles in the unstable surface layer. Boundary-Layer Meteorol. 64 (4), 355–368.Google Scholar
Povitsky, A. & Morris, P. J. 2000 A higher-order compact method in space and time based on parallel implementation of the thomas algorithm. J. Comput. Phys. 161 (1), 182–203.CrossRefGoogle Scholar
Shah, S. & Bou-Zeid, E. 2014 Very-large-scale motions in the atmospheric boundary layer educed by snapshot proper orthogonal decomposition. Boundary-Layer Meteorol. 153 (3), 355–387.CrossRefGoogle Scholar
Sharma, V., Calaf, M., Lehning, M. & Parlange, M. B. 2016 Time-adaptive wind turbine model for an LES framework. Wind Energy 19 (5), 939–952.Google Scholar
Sharma, V., Parlange, M. B. & Calaf, M. 2016 Perturbations to the spatial and temporal characteristics of the diurnally-varying atmospheric boundary layer due to an extensive wind farm. Boundary-Layer Meteorol. 162 (2), 255–282.CrossRefGoogle Scholar
StMartin, C. M., Lundquist, J. K., Clifton, A., Poulos, G. S. & Schreck, S. J. 2016 Wind turbine power production and annual energy production depend on atmospheric stability and turbulence. Wind Energy Sci. 1 (2), 221–236.Google Scholar
Stull, R. B. 1988 An Introduction to Boundary Layer Meteorology. Springer.Google Scholar
VerHulst, C. & Meneveau, C. 2014 Large eddy simulation study of the kinetic energy entrainment by energetic turbulent flow structures in large wind farms. Phys. Fluids 26, 025113.Google Scholar
Wharton, S. & Lundquist, J. K. 2012 Atmospheric stability affects wind turbine power collection. Environ. Res. Lett. 7 (1), 014005.Google Scholar
Wu, Y.-T. & Porté-agel, F. 2011 Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-Layer Meteorol. 138, 345–366.Google Scholar
Zhang, W., Markfort, C. D. & Porté-Agel, F. 2013 Wind-turbine wakes in a convective boundary layer: a wind-tunnel study. Boundary-Layer Meteorol. 146 (2), 161–179.CrossRefGoogle Scholar