A physics-based model for wind turbine wake expansion in the atmospheric boundary layer

Vahidi, Dara; Porté‐Agel, Fernando

doi:10.1017/jfm.2022.443

Cited by 20 publications

(8 citation statements)

References 58 publications

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“…Following [5,30], the end of the near wake is assumed to be the position where the theoretical and experimental velocity deficit maximum on the escarpments become equal. The near wake length obtained by this criterion is very similar to the one obtained from theoretical relations derived for flat terrain [5,31]. In order to use Equation ( 13), we need to define position 4 in Figure 1.…”

Section: Model Validationsupporting

confidence: 72%

An Analytical Model for Wind Turbine Wakes under Pressure Gradient

Dar

Porté‐Agel

2022

Energies

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In this study, we present an analytical modeling framework for wind turbine wakes under an arbitrary pressure gradient imposed by the base flow. The model is based on the conservation of the streamwise momentum and self-similarity of the wake velocity deficit. It builds on the model proposed by Shamsoddin and Porté-Agel, which only accounted for the imposed pressure gradient in the far wake. The effect of the imposed pressure gradient on the near wake velocity is estimated by using Bernoulli’s equation. Using the estimated near wake velocity as the starting point, the model then solves an ordinary differential equation to compute the streamwise evolution of the maximum velocity deficit in the turbine far wake. The model is validated against experimental data of wind turbine wakes on escarpments of varying geometries. In addition, a comparison is performed with a pressure gradient model which only accounts for the imposed pressure gradient in the far wake, and with a model that does not account for any imposed pressure gradient. The new model is observed to agree well with the experimental data, and it outperforms the other two models tested in the study for all escarpment cases.

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Section: Model Validationsupporting

confidence: 72%

An Analytical Model for Wind Turbine Wakes under Pressure Gradient

Dar

Porté‐Agel

2022

Energies

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“…Following the study for ABL flows with higher turbulence intensity, in Ref. [9], the wake growth rate is modeled as k w = 0.33 I u . Similarly, for SBL flows with lower I u , the growth rate is assumed to tend toward a constant value, k w = 0.021, as shear-generated turbulence becomes dominant over turbulent entrainment mediated by ABL turbulence [9].…”

Section: A Comprehensive Gaussian Wake Model For Wind Turbine Wakes I...mentioning

confidence: 99%

“…[9], the wake growth rate is modeled as k w = 0.33 I u . Similarly, for SBL flows with lower I u , the growth rate is assumed to tend toward a constant value, k w = 0.021, as shear-generated turbulence becomes dominant over turbulent entrainment mediated by ABL turbulence [9]. To model k w across both low and high I u regimes, the following empirical model for k w is used [10]:…”

Section: A Comprehensive Gaussian Wake Model For Wind Turbine Wakes I...mentioning

confidence: 99%

Analytical Wake Modeling in Atmospheric Boundary Layers: Accounting for Wind Veer and Thermal Stratification

Narasimhan,

Gayme,

Meneveau

2024

J. Phys.: Conf. Ser.

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Reliable characterization of wind turbine wakes in the presence of Atmospheric Boundary Layer (ABL) flows is crucial to accurately predict wind farm performance. Wind veering in the ABL shears the wake in the lateral direction, and wind veer strength depends on the thermal stability of the ABL. Analytical wake modeling approaches must capture these ABL effects to ensure correct prediction of the wake structure under varied atmospheric conditions. To this end, a new physics-based analytical wake model is developed in this study that is capable of predicting the shape of wakes influenced by wind veer and thermal stratification effects. This model combines a novel ABL wind field model with the Gaussian wake model. The new ABL wind model is capable of predicting both the streamwise and spanwise velocity components in conventionally neutral (CNBL) and stable (SBL) ABL flows. The analytical expressions for both of these horizontal velocity components adhere to Monin-Obukhov Similarity Theory (MOST) in the surface layer, while capturing wind veering in the outer layer of the ABL. Incorporating this ABL model with the Gaussian wake model predicts laterally deflected wake shapes in a fully predictive and self-consistent fashion for a wide range of atmospheric conditions. The results also demonstrate that the enhanced wake model gives improved predictions relative to Large Eddy Simulations of power losses due to wake interactions under strongly stably stratified atmospheric conditions, where wind veer effects are dominant.

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“…Abkar & Porté-Agel 2015; Xie & Archer 2015; Pedersen et al. 2022; Vahidi & Porté-Agel 2022) or to capture effects of yaw angle (e.g. Bastankhah & Porté-Agel 2016; King et al.…”

Section: Introductionmentioning

confidence: 99%

A fast-running physics-based wake model for a semi-infinite wind farm

Bastankhah,

Mohammadi,

Lees

et al. 2024

J. Fluid Mech.

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This paper presents a new generation of fast-running physics-based models to predict the wake of a semi-infinite wind farm, extending infinitely in the lateral direction but with finite size in the streamwise direction. The assumption of a semi-infinite wind farm enables concurrent solving of the laterally averaged momentum equations in both streamwise and spanwise directions. The developed model captures important physical phenomena such as vertical top-down transport of energy into the farm, variable wake recovery rate due to the farm-generated turbulence and also wake deflection due to turbine yaw misalignment and Coriolis force. Of special note is the model's capability to predict and shed light on the counteracting effect of Coriolis force causing wake deflections in both positive and negative directions. Moreover, the impact of wind farm layout configuration on the flow distribution is modelled through a parameter called the local deficit coefficient. Model predictions were validated against large-eddy simulations extending up to 45 km downstream of wind farms. Detailed analyses were performed to study the impacts of various factors such as incoming turbulence, wind farm size, inter-turbine spacing and wind farm layout on the farm wake.

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A physics-based model for wind turbine wake expansion in the atmospheric boundary layer

Cited by 20 publications

References 58 publications

An Analytical Model for Wind Turbine Wakes under Pressure Gradient

An Analytical Model for Wind Turbine Wakes under Pressure Gradient

Analytical Wake Modeling in Atmospheric Boundary Layers: Accounting for Wind Veer and Thermal Stratification

A fast-running physics-based wake model for a semi-infinite wind farm

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