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Wind turbine wakes over hills

Published online by Cambridge University Press:  19 September 2018

Sina Shamsoddin  and
Fernando Porté-Agel Open the ORCID record for Fernando Porté-Agel [Opens in a new window]
Sina Shamsoddin
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Wind Engineering and Renewable Energy Laboratory (WIRE), EPFL-ENAC-IIE-WIRE, CH-1015 Lausanne, Switzerland
Fernando Porté-Agel*
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Wind Engineering and Renewable Energy Laboratory (WIRE), EPFL-ENAC-IIE-WIRE, CH-1015 Lausanne, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

Understanding and predicting the behaviour of wind turbine wake flows over hills is important for optimal design of wind-farm configurations on topography. In this study, we present an analytical modelling framework together with large-eddy simulation (LES) results to investigate turbine wakes over two-dimensional hills. The analytical model consists of two steps. In the first step, we deal with the effect of the pressure gradient on the wake evolution; and in the second step, we consider the effect of the hill-induced streamline distortion on the wake. This model enables us to obtain the wake recovery rate, the mean velocity and velocity deficit profiles and the wake trajectory in the presence of the hill. Moreover, we perform LES to test our model and also to obtain new complementary insight about such flows. Especially, we take advantage of the LES data to perform a special analysis of the behaviour of the wake on the leeward side of the hill. It is found that the mainly favourable pressure gradient on the windward side of the hill accelerates the wake recovery and the adverse pressure gradient on the leeward side decelerates it. The wake trajectory for a hill of the same height as the turbine’s hub height is found to closely follow the hill profile on the windward side, but it maintains an almost constant elevation (a horizontal line) downstream of the hilltop. The trajectory of the wake on the leeward side is also studied for a limiting case of an escarpment, and it is shown that an internal boundary layer forms on the plateau which leads to an upward displacement of the wake centre. Finally, a parametric study of the position of the turbine with respect to the hill is performed to further elucidate the effect of the hill-induced pressure gradient on the wind turbine wake recovery.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 671 - 702
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© 2018 Cambridge University Press 

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References

Albertson, J. D. & Parlange, M. B. 1999 Surfaces length scales and shear stress: implications for land–atmosphere interactions over complex terrain. Water Resour. Res. 35, 2121–2132.Google Scholar
Ansorge, T., Fallen, M., Günther, P., Ruh, C. & Wolfanger, T. 1994 Numerical simulation of wake-effects in complex terrain and application of a Reynolds-stress turbulence model. In Proc. EWEC (ed. Tsipouridis, J.), vol. 94, pp. 448–453. Hellenic Wind Energy Association and European Wind Energy Association.Google Scholar
Baskaran, V., Smits, A. J. & Joubert, P. N. 1987 A turbulent flow over a curved hill. Part 1. Growth of an internal boundary layer. J. Fluid Mech. 182, 47–83.Google Scholar
Baskaran, V., Smits, A. J. & Joubert, P. N. 1991 A turbulent flow over a curved hill. Part 2. Effects of streamline curvature and streamwise pressure gradient. J. Fluid Mech. 232, 377–402.Google Scholar
Bastankhah, M. & Porté-Agel, F. 2016 Experimental and theoretical study of wind turbine wakes in yawed conditions. J. Fluid Mech. 806, 506–541.Google Scholar
Belcher, S. E. 1999 Wave growth by non-separated sheltering. Eur. J. Mech. (B/Fluids) 18 (3), 447–462.Google Scholar
Belcher, S. E. & Hunt, J. C. R. 1998 Turbulent flow over hills and waves. Annu. Rev. Fluid Mech. 30 (1), 507–538.Google Scholar
Belcher, S. E., Newley, T. M. J. & Hunt, J. C. R. 1993 The drag on an undulating surface induced by the flow of a turbulent boundary layer. J. Fluid Mech. 249, 557–596.Google Scholar
Berg, J., Mann, J., Bechmann, A., Courtney, M. & Jørgensen, H. 2011 The Bolund experiment. Part I. Flow over a steep, three-dimensional hill. Boundary-Layer Meteorol. 141, 219–243.Google Scholar
Berg, J., Troldborg, N., Sørensen, N. N., Patton, E. G. & Sullivan, P. P. 2017 Large-eddy simulation of turbine wake in complex terrain. J. Phys.: Conf. Ser. 854 (1), 012003.Google Scholar
Bowen, A. J. & Mortensen, N. G.2004 WAsP prediction errors due to site orography. Tech. Rep. Risø-R-995(EN). Risø National Laboratory, Roskilde, Denmark.Google Scholar
Britter, R. E., Hunt, J. C. R. & Richards, K. J. 1981 Air flow over a two-dimensional hill: studies of velocity speed-up, roughness effects and turbulence. Q. J. R. Meteorol. Soc. 107, 91–110.Google Scholar
Castellani, F., Astolfi, D., Burlando, M. & Terzi, L. 2015 Numerical modelling for wind farm operational assessment in complex terrain. J. Wind Engng Ind. Aerodyn. 147 (Suppl. C), 320–329.Google Scholar
Castellani, F., Astolfi, D., Mana, M., Piccioni, E., Becchetti, M. & Terzi, L. 2017 Investigation of terrain and wake effects on the performance of wind farms in complex terrain using numerical and experimental data. Wind Energy 20 (7), 1277–1289; we.2094.Google Scholar
Chaviaropoulos, P. K. & Douvikas, D. J. 1999 Mean wind field prediction over complex terrain in the presence of wind turbine (s). In EWEC-CONFERENCE (ed. Petersen, E. L., Jensen, P., Rave, K., Helm, P. & Ehmann, H.), pp. 1208–1211.Google Scholar
Corby, G. A. 1954 The airflow over mountains: a review of the state of current knowledge. Q. J. R. Meteorol. Soc. 80, 491–521.Google Scholar
Cortelezzi, L. & Karagozian, A. R. 2001 On the formation of the counter-rotating vortex pair in transverse jets. J. Fluid Mech. 446, 347–373.Google Scholar
Crespo, A. & Hernández, J. 1986 A numerical model of wind turbine wakes and wind farms. In European Wind Energy Conference EWEC (ed. Palz, W. & Sesto, E.), vol. 2, pp. 111–115.Google Scholar
Crespo, A., Manuel, F., Grau, J. C. & Hernández, J. 1993 Modelization of wind farms in complex terrain: application to the Monteahumada wind farm. In Proceedings of the 1993 European Community Wind Energy Conference (ed. Garrad, A. D., Palz, W. & Scheller, S.), pp. 436–439. H. S. Stephens & Associates.Google Scholar
Diebold, M., Higgins, C., Fang, J., Bechmann, A. & Parlange, M. B. 2013 Flow over hills: a large-eddy simulation of the bolund case. Boundary-Layer Meteorol. 148 (1), 177–194.Google Scholar
Emeis, S. 2013 Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation. Springer.Google Scholar
Emeis, S., Frank, H. P. & Fiedler, F. 1995 Modification of air flow over an escarpment: results from the Hjardemål experiment. Boundary-Layer Meteorol. 74 (1), 131–161.Google Scholar
Fearn, R. & Weston, R. 1974 Vorticity associated with a jet in a cross flow. AIAA J. 12 (12), 1666–1671.Google Scholar
García-Villalba, M., Li, N., Rodi, W. & Leschziner, M. A. 2009 Large-eddy simulation of separated flow over a three-dimensional axisymmetric hill. J. Fluid Mech. 627, 55–96.Google Scholar
Garratt, J. R. 1994 The Atmospheric Boundary Layer. Cambridge University Press.Google Scholar
Garratt, J. R. 1990 The internal boundary layer: a review. Boundary-Layer Meteorol. 50 (1), 171–203.Google Scholar
Giometto, M. G., Katul, G. G., Fang, J. & Parlange, M. B. 2017 Direct numerical simulation of turbulent slope flows up to Grashof number gr = 2. 1 × 1011 . J. Fluid Mech. 829, 589–620.Google Scholar
Gong, W., Taylor, P. A. & Dörnbrack, A. 1996 Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves. J. Fluid Mech. 312, 1–37.Google Scholar
Günther, P., Fallen, M. & Wolfanger, T. 1993 Numerical wake simulation of a HAWT considering topography and using a mesoscale turbulence model. In Proc. 1993 European Community Wind Energy Conf (ed. Garrad, A. D., Palz, W. & Scheller, S.), pp. 448–450. H. S. Stephens & Associates.Google Scholar
Gutmark, E. J., Ibrahim, I. M. & Murugappan, S. 2008 Circular and noncircular subsonic jets in cross flow. Phys. Fluids 20 (7), 075110.Google Scholar
Helmis, C. G., Papadopoulos, K. H., Asimakopoulos, D. N., Papageorgas, P. G. & Soilemes, A. T. 1995 An experimental study of the near wake structure of a wind turbine operating over complex terrain. Solar Energy 54 (6), 413–428.Google Scholar
Hemon, A., Huberson, S. & Zervos, A. 1991 Numerical study of wind turbine operation in complex terrain. In Proceedings of the 13th British Wind Energy Association (BWEA) Conference, Wind Energy Conversion (ed. Quarton, D. C. & Fenton, V. C.), pp. 343–349. Mechanical Engineering Publications.Google Scholar
Hunt, J. C. R., Leibovich, S. & Richards, K. J. 1988 Turbulent shear flow over low hills. Q. J. R. Meteorol. Soc. 114, 1435–1470.Google Scholar
Hyvärinen, A. & Segalini, A. 2017a Effects from complex terrain on wind-turbine performance. J. Energy Resour. Technol. 139 (5), 051205.Google Scholar
Hyvärinen, A. & Segalini, A. 2017b Qualitative analysis of wind-turbine wakes over hilly terrain. J. Phys.: Conf. Series 854 (1), 012023.Google Scholar
Iizuka, S. & Kondo, H. 2004 Performance of various sub-grid scale models in large-eddy simulation of turbulent flow over complex terrain. Atmos. Environ. 38, 7083–7091.Google Scholar
Ishihara, T., Hibi, K. & Oikawa, S. 1999 A wind tunnel study of turbulent flow over a three-dimensional steep hill. J. Wind Engng Ind. Aerodyn. 83, 95–107.Google Scholar
Ivanova, L. A. & Nadyozhina, E. D. 2000 Numerical simulation of wind farm influence on wind flow. Wind Engng 24 (4), 257–269.Google Scholar
Jackson, N. A. 1976 The propagation of modified flow downstream of a change in roughness. Q. J. R. Meteorol. Soc. 102 (434), 924–933.Google Scholar
Jackson, P. S. & Hunt, J. C. R. 1975 Turbulent wind flow over a low hill. Q. J. R. Meteorol. Soc. 101, 929–955.Google Scholar
Kamotani, Y. & Greber, I. 1972 Experiments on a turbulent jet in a cross flow. AIAA J. 10 (11), 1425–1429.Google Scholar
Kelso, R. M., Lim, T. T. & Perry, A. E. 1996 An experimental study of round jets in cross-flow. J. Fluid Mech. 306, 111–144.Google Scholar
Liu, X., Thomas, F. O. & Nelson, R. C. 2002 An experimental investigation of the planar turbulent wake in constant pressure gradient. Phys. Fluids 14 (8), 2817–2838.Google Scholar
Mason, P. J. & Sykes, R. I. 1979 Flow over an isolated hill of moderate slope. Q. J. R. Meteorol. Soc. 105, 383–395.Google Scholar
Migoya, E., Crespo, A., García, J., Moreno, F., Manuel, F. J. & Costa, A. 2007 Comparative study of the behavior of wind-turbines in a wind farm. Energy 32 (10), 1871–1885.Google Scholar
Miyake, M.1965 Transformation of the atmospheric boundary layer over inhomogeneous surfaces. Tech. Rep. Sci. Rep. 5R-6. University of Washington.Google Scholar
Nakayama, A. 1987 Curvature and pressure-gradient effects on a small-defect wake. J. Fluid Mech. 175, 215–246.Google Scholar
Pasquill, F. 1972 Some aspects of boundary layer description. Q. J. R. Meteorol. Soc. 98 (417), 469–494.Google Scholar
Politis, E. S., Prospathopoulos, J., Cabezon, D., Hansen, K. S., Chaviaropoulos, P. K. & Barthelmie, R. J. 2012 Modeling wake effects in large wind farms in complex terrain: the problem, the methods and the issues. Wind Energy 15, 161–182.Google Scholar
Porté-Agel, F., Meneveau, C. & Parlange, M. B. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.Google Scholar
Porté-Agel, F., Wu, Y. T., Lu, H. & Conzemius, R. J. 2011 Large-eddy simulation of atmospheric boundary layer flow through wind turbines and wind farms. J. Wind Engng Ind. Aerodyn. 99 (4), 154–168.Google Scholar
Razavi, A. & Sarkar, P. P. 2018 Laboratory study of topographic effects on the near-surface tornado flow field. Boundary-Layer Meteorol 168 (2), 189–212.Google Scholar
Rogers, M. M. 2002 The evolution of strained turbulent plane wakes. J. Fluid Mech. 463, 53–120.Google Scholar
Schulz, C., Klein, L., Weihing, P., Lutz, T. & Krämer, E. 2014 CFD studies on wind turbines in complex terrain under atmospheric inflow conditions. J. Phys.: Conf. Series 524 (1), 012134.Google Scholar
Segalini, A. 2017 Linearized simulation of flow over wind farms and complex terrains. Phil. Trans. R. Soc. Lond. A 375 (2091), 20160099. http://rsta.royalsocietypublishing.org/content/375/2091/20160099.full.pdf.Google Scholar
Segalini, A. & Inghels, P. 2014 Confinement effects in wind-turbine and propeller measurements. J. Fluid Mech. 756, 110–129.Google Scholar
Shamsoddin, S. & Porté-Agel, F. 2014 Large eddy simulation of vertical axis wind turbine wakes. Energies 7 (2), 890–912.Google Scholar
Shamsoddin, S. & Porté-Agel, F. 2016 A large-eddy simulation study of vertical axis wind turbine wakes in the atmospheric boundary layer. Energies 9 (5), 366.Google Scholar
Shamsoddin, S. & Porté-Agel, F. 2017a Large-eddy simulation of atmospheric boundary-layer flow through a wind farm sited on topography. Boundary-Layer Meteorol. 163 (1), 1–17.Google Scholar
Shamsoddin, S. & Porté-Agel, F. 2017b Turbulent planar wakes under pressure gradient conditions. J. Fluid Mech. 830, R4.Google Scholar
Shamsoddin, S. & Porté-Agel, F. 2018 A model for the effect of pressure gradient on turbulent axisymmetric wakes. J. Fluid Mech. 837, R3.Google Scholar
Stefanatos, N. Ch., Morfiadakis, E. E. & Glinou, G. L. 1996 Wake measurements in complex terrain. In Proceedings of the 1996 European Union Wind Energy Conference, Göteborg, Sweden (ed. Zervos, A., Ehmann, H. & Helm, P.), pp. 773–777. H. S. Stephens & Associates.Google Scholar
Stefanatos, N. Ch., Voutsinas, S. G., Rados, K. G. & Zervos, A. 1994 A combined experimental and numerical investigation of wake effects in complex terrain. In Proceedings of EWEC (ed. Tsipouridis, J. L.), vol. 94, pp. 484–490. Hellenic Wind Energy Association and European Wind Energy Association.Google Scholar
Stoll, R. & Porté-Agel, F. 2006 Dynamic subgrid-scale models for momentum and scalar fluxes in large-eddy simulation of neutrally stratified atmospheric boundary layers over heterogeneous terrain. Water Resour. Res. 42, W01409.Google Scholar
Sykes, R. I. 1980 An asymptotic theory of incompressible turbulent boundary-layer flow over a small hump. J. Fluid Mech. 101, 647–670.Google Scholar
Taylor, G. J. & Smith, D. 1991 Wake measurements over complex terrain. In Proceedings of the 13th British Wind Energy Association (BWEA) Conference, Wind Energy Conversion (ed. Quarton, D. C. & Fenton, V. C.), pp. 335–342. Mechanical Engineering Publications.Google Scholar
Taylor, P. A. & Teunissen, H. W. 1987 The Askervein Hill project: overview and background data. Boundary-Layer Meteorol. 39, 15–39.Google Scholar
Taylor, P. A., Walmsley, J. L. & Salmon, J. R. 1983 A simple model of neutrally stratified boundary-layer flow over real terrain incorporating wavenumber-dependent scaling. Boundary-Layer Meteorol. 26, 169–189.Google Scholar
Thomas, F. O. & Liu, X. 2004 An experimental investigation of symmetric and asymmetric turbulent wake development in pressure gradient. Phys. Fluids 16 (5), 1725–1745.Google Scholar
Tian, W., Ozbay, A., Yuan, W., Sarkar, P. & Hu, H. 2013 An experimental study on the performances of wind turbines over complex terrains. In 51st Am. Inst. Aeronaut Astronaut Aerospace Sci. Mtg. Grapevine, Texas, USA.Google Scholar
Tseng, Y.-H., Meneveau, C. & Parlange, M. B. 2006 Modeling flow around bluff bodies and predicting urban dispersion using large eddy simulation. Environ. Sci. Technol. 40, 2653–2662.Google Scholar
Voutsinas, S. G., Rados, K. G. & Zervos, A. 1990 The effect of the non-uniformity of the wind velocity field in the optimal design of wind parks. In Proceedings of the 1990 European Community Wind Energy Conference (ed. Palz, W.), pp. 181–185. H. S. Stephens & Associates.Google Scholar
Wan, F. & Porté-Agel, F. 2011 Large-eddy simulation of stably-stratified flow over a steep hill. Boundary-Layer Meteorol. 138 (3), 367–384.Google Scholar
Wan, F., Porté-Agel, F. & Stoll, R. 2007 Evaluation of dynamic subgrid-scale models in large-eddy simulations of neutral turbulent flow over a two-dimensional sinusoidal hill. Atmos. Environ. 41 (13), 2719–2728.Google Scholar
Wood, N. 2000 Wind flowover complex terrain: a historical perspective and the prospect for large-eddy modelling. Boundary-Layer Meteorol. 96, 11–32.Google Scholar
Wu, Y. T. & Porté-Agel, F. 2011 Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-Layer Meteorol. 138 (3), 345–366.Google Scholar
Wu, Y. T. & 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.Google Scholar
Wurtele, M. G., Sharman, R. D. & Datta, A. 1996 Atmospheric lee waves. Annu. Rev. Fluid Mech. 28, 429–476.Google Scholar
Xu, D., Ayotte, K. W. & Taylor, P. A. 1994 Development of a non-linear mixed spectral finite difference model for turbulent boundary layer flow over topography. Boundary-Layer Meteorol. 70, 341–367.Google Scholar
Xu, D. & Taylor, P. A. 1992 A non-linear extension of the mixed spectral finite difference model for neutrally stratified turbulent flow over topography. Boundary-Layer Meteorol. 59, 177–186.Google Scholar
Yang, X., Howard, K. B., Guala, M. & Sotiropoulos, F. 2015 Effects of a three-dimensional hill on the wake characteristics of a model wind turbine. Phys. Fluids 27 (2), 025103.Google Scholar
Yang, X., Sotiropoulos, F., Conzemius, R. J., Wachtler, J. N. & Strong, M. B. 2014 Large-eddy simulation of turbulent flow past wind turbines/farms: the virtual wind simulator (VWiS). Wind Energy 18, 2025–2045.Google Scholar
Zheng, K., Tian, W., Qin, J. & Hu, H. 2017 Investigation of wind turbine wakes over complex terrain based on actuator disk method. In 35th AIAA Applied Aerodynamics Conference, AIAA AVIATION Forum, AIAA Paper 2017–4073, American Institute of Aeronautics and Astronautics.Google Scholar