Geostrophic drag law for conventionally neutral atmospheric boundary layers revisited

Liu, Luoqin; Gadde, Srinidhi Nagarada; Stevens, Richard J. A. M.

doi:10.1002/qj.3949

Cited by 25 publications

(41 citation statements)

References 61 publications

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“…It is demonstrated that and are well parametrized by a function that depends only on , similar to what is observed in the classical GDL for flow over flat terrain (Zilitinkevich & Esau 2005; Liu et al. 2021 a ). This confirms that the similarity arguments apply for flow over extended wind farm arrays, even though their physics are different.…”

Section: Geostrophic Drag Law For Extended Wind Farmssupporting

confidence: 65%

“…Typical values for the GDL coefficients and reported from meteorological observations are and (Hess & Garratt 2002). It has been shown that, for conventionally neutral ABLs, the coefficients and only depend on the Zilitinkevich number (Esau 2004; Kadantsev, Mortikov & Zilitinkevich 2021; Liu, Gadde & Stevens 2021 a , b ; Liu & Stevens 2022). Here is the free-atmosphere Brunt–Väisälä frequency, is the gravity acceleration, is the free-atmosphere lapse rate and is the reference potential temperature.…”

Section: Introductionmentioning

confidence: 99%

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Analytical model of fully developed wind farms in conventionally neutral atmospheric boundary layers

Liu

et al. 2022

J. Fluid Mech.

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The wind energy industry relies on computationally efficient engineering-type models to design wind farms. Typically these models do not account for the effect of atmospheric stratification in either the boundary layer or the free atmosphere. This study proposes a new analytical model for fully developed wind-turbine arrays in conventionally neutral atmospheric boundary layers frequently encountered in nature. The model captures the effect of the free-atmosphere stratification, Coriolis force, wind farm layout and turbine operating condition on the wind farm performance. The model is developed based on the physical insight derived from large-eddy simulations. We demonstrate that the geostrophic drag law (GDL) for flow over flat terrain can be extended to flow over fully developed wind farm arrays. The presence of a vast wind farm significantly increases the wind farm friction velocity compared with flow over flat terrain, which is modelled by updated coefficients in the GDL. The developed model reliably captures the vertical wind speed profile inside the wind farm. Furthermore, the power production trends observed in simulations are reliably reproduced. The wind farm performance, normalized by the geostrophic wind speed, decreases as the free-atmosphere thermal stability increases or the Coriolis force decreases. In addition, we find that the optimal wind farm performance is obtained at a lower thrust coefficient than the Betz limit, which indicates that optimal operating conditions for turbines in a wind farm are different than for a single turbine.

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Section: Geostrophic Drag Law For Extended Wind Farmssupporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Analytical model of fully developed wind farms in conventionally neutral atmospheric boundary layers

Liu

et al. 2022

J. Fluid Mech.

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“…The flow is initialized with uniform geostrophic wind speed and a linear potential temperature profile with a constant gradient [35,44]. The simulations are performed with an in-house code [50][51][52][53][54][55], which employs a pseudospectral discretization in the horizontal directions and a second-order finite difference method in the vertical direction. We employ the advanced anisotropic minimum dissipation model to parametrize the subgrid scale shear stress and potential temperature flux [56].…”

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confidence: 99%

Universal Wind Profile for Conventionally Neutral Atmospheric Boundary Layers

2021

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Conventionally neutral atmospheric boundary layers (CNBLs), which are characterized with zero surface potential temperature flux and capped by an inversion of potential temperature, are frequently encountered in nature. Therefore, predicting the wind speed profiles of CNBLs is relevant for weather forecasting, climate modeling, and wind energy applications. However, previous attempts to predict the velocity profiles in CNBLs have had limited success due to the complicated interplay between buoyancy, shear, and Coriolis effects. Here, we utilize ideas from the classical Monin-Obukhov similarity theory in combination with a local scaling hypothesis to derive an analytic expression for the stability correction function ψ ¼ −c ψ ðz=LÞ 1=2 , where c ψ ¼ 4.2 is an empirical constant, z is the height above ground, and L is the local Obukhov length based on potential temperature flux at that height, for CNBLs. An analytic expression for this flux is also derived using dimensional analysis and a perturbation method approach. We find that the derived profile agrees excellently with the velocity profile in the entire boundary layer obtained from high-fidelity large eddy simulations of typical CNBLs.

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“…For a detailed description and validation of our code we refer the reader to Refs. [31][32][33] The wind turbines are modeled using an actuator disk approach in which the free-stream velocity U ∞ is used to calculate the turbine force F wt…”

Section: A Numerical Methodsmentioning

confidence: 99%

“…Following Abkar and Porté-Agel [41], we first perform time-averaging of the filtered momentum equation [31][32][33],…”

Section: Kinetic Energy Budget Analysismentioning

confidence: 99%

Enhanced wind-farm performance using windbreaks

Liu,

Stevens

2021

Preprint

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The flow speed-up generated by windbreaks can be used to increase the power production of wind turbines. However, due to the increased drag imposed by the windbreaks, their use in large wind turbine arrays has been questioned. We use large eddy simulations to show that windbreaks can increase the power production of large wind farms. A crucial finding is that windbreaks in a wind farm should be much lower than for a single turbine case. In fact, the optimal windbreak for an isolated turbine can reduce wind farm performance. The optimal windbreak height in a wind farm namely depends on the right balance between flow speed-up over the windbreak and the drag imposed by all windbreaks in the farm. The increased performance is a result of the favorable total pressure flux created by the windbreaks.

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Geostrophic drag law for conventionally neutral atmospheric boundary layers revisited

Cited by 25 publications

References 61 publications

Analytical model of fully developed wind farms in conventionally neutral atmospheric boundary layers

Analytical model of fully developed wind farms in conventionally neutral atmospheric boundary layers

Universal Wind Profile for Conventionally Neutral Atmospheric Boundary Layers

Enhanced wind-farm performance using windbreaks

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