Gravity Waves and Wind-Farm Efficiency in Neutral and Stable Conditions

Springer Science and Business Media LLC - Tập 166 - Trang 269-299 - 2017
Dries Allaerts, Johan Meyers1
1Department of Mechanical Engineering, KU Leuven, Leuven, Belgium

Tóm tắt

We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.

Tài liệu tham khảo

Abkar M, Sharifi A, Porté-Agel F (2016) Wake flow in a wind farm during a diurnal cycle. J Turbul 17(4):420–441 Allaerts D (2016) Large-eddy simulation of wind farms in conventionally neutral and stable atmospheric boundary layers. PhD thesis. KU Leuven Allaerts D, Meyers J (2015) Large eddy simulation of a large wind-turbine array in a conventionally neutral atmospheric boundary layer. Phys Fluids 27(065):108 Allaerts D, Meyers J (2017) Boundary-layer development and gravity waves in conventionally neutral wind farms. J Fluid Mech 814:95–130 André JC, Mahrt L (1982) The nocturnal surface inversion and influence of clear-air radiative cooling. J Atmos Sci 39(4):864–878 Barthelmie RJ, Hansen K, Frandsen ST, Rathmann O, Schepers JG, Schlez W, Phillips J, Rados K, Zervos A, Politis ES, Chaviaropoulos PK (2009) Modelling and measuring flow and wind turbine wakes in large wind farms offshore. Wind Energy 12(5):431–444 Beare RJ, Macvean MK, Holtslag AAM, Cuxart J, Esau I, Golaz JC, Jimenez MA, Khairoutdinov M, Kosović B, Lewellen D, Lund TS, Lundquist JK, Mccabe A, Moene AF, Noh Y, Raasch S, Sullivan PP (2006) An intercomparison of large-eddy simulations of the stable boundary layer. Boundary-Layer Meteorol 118(2):247–272 Blackadar AK (1957) Boundary layer wind maxima and their significance for the growth of nocturnal inversions. Bull Am Meteorol Soc 38:283–290 Blümel K (2000) An approximate analytical solution of flux-profile relationships for the atmospheric surface layer with different momentum and heat roughness lengths. Boundary-Layer Meteorol 97(2):251–271 Bokharaie VS, Bauweraerts P, Meyers J (2016) Wind-farm layout optimisation using a hybrid Jensen-LES approach. Wind Energy Sci 1(2):311–325 Bou-Zeid E, Meneveau C, Parlange M (2005) A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys Fluids 17(2):025105 Brinkmann WAR (1974) Strong downslope winds at Boulder, Colorado. Mon Weather Rev 102(8):592–602 Businger JA, Wyngaard JC, Izumi Y, Bradley EF (1971) Flux-profile relationships in the atmospheric surface layer. J Atmos Sci 28(2):181–189 Calaf M, Meneveau C, Meyers J (2010) Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys Fluids 22:015110 Cortina G, Calaf M, Cal RB (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 1:074402 Csanady GT (1974) Equilibrium theory of the planetary boundary layer with an inversion lid. Boundary-Layer Meteorol 6(1–2):63–79 Deardorff JW (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol 18(4):495–527 Dörenkämper M, Witha B, Steinfeld G, Heinemann D, Kühn M (2015) The impact of stable atmospheric boundary layers on wind-turbine wakes within offshore wind farms. J Wind Eng Ind Aerodyn 144:146–153 Doyle JD, Shapiro MA, Jiang Q, Bartels DL (2005) Large-amplitude mountain wave breaking over Greenland. J Atmos Sci 62(9):3106–3126 España G, Aubrun S, Loyer S, Devinant P (2011) Spatial study of the wake meandering using modelled wind turbines in a wind tunnel. Wind Energy 14(7):923–937 Frandsen S, Barthelmie R, Pryor S, Rathmann O, Larsen S, Højstrup J, Thøgersen M (2006) Analytical modelling of wind speed deficit in large offshore wind farms. Wind Energy 9(1–2):39–53 Goit JP, Meyers J (2015) Optimal control of energy extraction in wind-farm boundary layers. J Fluid Mech 768:5–50 Goit JP, Munters W, Meyers J (2016) Optimal coordinated control of power extraction in LES of a wind farm with entrance effects. Energies 9(1):29 Jiang Q, Doyle JD (2008) On the diurnal variation of mountain waves. J Atmos Sci 65(4):1360–1377 Jimenez A, Crespo A, Migoya E, Garcia J (2007) Advances in large-eddy simulation of a wind turbine wake. J Phys Conf Ser 75(1):012041 Kosović B, Curry JA (2000) A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J Atmos Sci 57(8):1052–1068 Kumar V, Kleissl J, Meneveau C, Parlange MB (2006) Large-eddy simulation of a diurnal cycle of the atmospheric boundary layer: atmospheric stability and scaling issues. Water Resour Res 42(6):1–18 Lange B, Larsen S, Højstrup J, Barthelmie R (2004) The influence of thermal effects on the wind speed profile of the coastal marine boundary layer. Boundary-Layer Meteorol 112(3):587–617 Lignarolo LEM, Mehta D, Stevens RJAM, Yilmaz AE, van Kuik G, Andersen SJ, Meneveau C, Ferreira CJ, Ragni D, Meyers J, van Bussel GJW, Holierhoek J (2016) Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine. Renew Energy 94:510–523 Lu H, Porté-Agel F (2011) Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer. Phys Fluids 23(6):065101 Martínez-Tossas LA, Churchfield MJ, Leonardi S (2015) Large eddy simulations of the flow past wind turbines: actuator line and disk modeling. Wind Energy 18(6):1047–1060 Meyers J, Meneveau C (2010) Large eddy simulations of large wind-turbine arrays in the atmospheric boundary layer. AIAA paper no 2010-827, pp 1–10 Meyers J, Meneveau C (2013) Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms. J Fluid Mech 715:335–358 Meyers J, Sagaut P (2007) Evaluation of Smagorinsky variants in large-eddy simulations of wall-resolved plane channel flows. Phys Fluids 19(9):095105 Moeng CH (1984) A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J Atmos Sci 41(13):2052–2062 Munters W, Meneveau C, Meyers J (2016) Turbulent inflow precursor method with time-varying direction for large-eddy simulations and applications to wind farms. Boundary-Layer Meteorol 159(2):305–328 Poulos GS, Blumen W, Fritts DC, Lundquist JK, Sun J, Burns SP, Nappo C, Banta R, Newsom R, Cuxart J, Terradellas E, Balsley B, Jensen M (2002) CASES-99: a comprehensive investigation of the stable nocturnal boundary layer. Bull Am Meteorol Soc 83(4):555–581 Shapiro A, Fedorovich E (2010) Analytical description of a nocturnal low-level jet. Q J R Meteorol Soc 136(650):1255–1262 Sharma V, Parlange MB, Calaf M (2017) 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 Smedman AS (1991) Some turbulence characteristics in stable atmospheric boundary layer flow. J Atmos Sci 48(6):856–868 Smedman AS, Bergström H, Grisogono B (1997) Evolution of stable internal boundary layers over a cold sea. J Geophys Res 102(C1):1091–1099 Smith RB (2007) Interacting mountain waves and boundary layers. J Atmos Sci 64:594–607 Smith RB (2010) Gravity wave effects on wind farm efficiency. Wind Energy 13(5):449–458 Stevens B, Moeng CH, Sullivan PP (2000) Entrainment and subgrid lengthscales in large-eddy simulations of atmospheric boundary-layer flows. In: Kerr RM, Kimura Y (eds) IUTAM symposium on developments in geophysical turbulence, fluid mechanics and its applications, vol 58. Springer, Amsterdam, pp 253–269 Stevens RJAM, Meneveau C (2017) Flow structure and turbulence in wind farms. Annu Rev Fluid Mech 49(1):311–339 Stevens RJAM, Graham J, Meneveau C (2014) A concurrent precursor inflow method for large eddy simulations and applications to finite length wind farms. Renew Energy 68:46–50 Taylor JR, Sarkar S (2007) Internal gravity waves generated by a turbulent bottom Ekman layer. J Fluid Mech 590:331–354 Taylor JR, Sarkar S (2008) Stratification effects in a bottom Ekman layer. J Phys Oceanogr 38(11):2535–2555 Tjernström M, Smedman AS (1993) The vertical turbulence structure of the coastal marine atmospheric boundary layer. J Geophys Res Oceans 98(C3):4809–4826 Valkonen T, Vihma T, Kirkwood S, Johansson MM (2010) Fine-scale model simulation of gravity waves generated by Basen nunatak in Antarctica. Tellus A 62(3):319–332 van de Wiel BJH, Moene AF, Steeneveld GJ, Baas P, Bosveld FC, Holtslag AAM (2010) A conceptual view on inertial oscillations and nocturnal low-level jets. J Atmos Sci 67(8):2679–2689 van der Laan MP, Sørensen NN (2016) Why the coriolis force turns a wind farm wake clockwise in the northern hemisphere. Wind Energy Sci Discuss 2016:1–12 Verstappen R, Veldman A (2003) Symmetry-preserving discretization of turbulent flow. J Comput Phys 187(1):343–368 Whiteman CD, Whiteman JD (1974) An historical climatology of damaging downslope windstorms at Boulder, Colorado. NOAA ERL336-APCL 35, National Oceanic and Atmospheric Administration, U.S. Department of Commerce Witha B, Steinfeld G, Dörenkämper M, Heinemann D (2014) Large-eddy simulation of multiple wakes in offshore wind farms. J Phys Conf Ser 555(1):012108 Wu YT, Porté-Agel F (2011) Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-Layer Meteorol 138(3):345–366 Wu YT, Porté-Agel F (2013) Simulation of turbulent flow inside and above wind farms: model validation and layout effects. Boundary-Layer Meteorol 146(2):181–205 Wyngaard JC (2010) Turbulence in the atmosphere. Cambridge University Press, Cambridge