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Linearized simulation of flow over wind farms and complex terrains
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. (STandUP ForWind, Sweden)ORCID iD: 0000-0001-8667-0520
2017 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 375, no 2091, 20160099Article in journal (Refereed) Published
Abstract [en]

The flow over complex terrains and wind farms is estimated here by numerically solving the linearized Navier-Stokes equations. The equations are linearized around the unperturbed incoming wind profile, here assumed logarithmic. The Boussinesq approximation is used to model the Reynolds stress with a prescribed turbulent eddy viscosity profile. Without requiring the boundary-layer approximation, two new linear equations are obtained for the vertical velocity and the wall-normal vorticity, with a reduction in the computational cost by a factor of 8 when compared with a primitive-variables formulation. The presence of terrain elevation is introduced as a vertical coordinate shift, while forestry or wind turbines are included as body forces, without any assumption about the wake structure for the turbines. The model is first validated against some available experiments and simulations, and then a simulation of a wind farm over a Gaussian hill is performed. The speed-up effect of the hill is clearly beneficial in terms of the available momentum upstream of the crest, while downstream of it the opposite can be said as the turbines face a decreased wind speed. Also, the presence of the hill introduces an additional spanwise velocity component that may also affect the turbines' operations. The linear superposition of the flow over the hill and the flow over the farm alone provided a first estimation of the wind speed along the farm, with discrepancies of the same order of magnitude for the spanwise velocity. Finally, the possibility of using a parabolic set of equations to obtain the turbulent kinetic energy after the linearized model is investigated with promising results. This article is part of the themed issue 'Wind energy in complex terrains'.

Place, publisher, year, edition, pages
ROYAL SOC , 2017. Vol. 375, no 2091, 20160099
Keyword [en]
wind farms, linearized methods, complex terrains
National Category
Energy Systems
Identifiers
URN: urn:nbn:se:kth:diva-206250DOI: 10.1098/rsta.2016.0099ISI: 000397879700004Scopus ID: 2-s2.0-85015884941OAI: oai:DiVA.org:kth-206250DiVA: diva2:1095310
Note

QC 20170512

Available from: 2017-05-12 Created: 2017-05-12 Last updated: 2017-06-30Bibliographically approved

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