The area localized coupled model for analytical mean flow prediction in arbitrary wind farm geometries

Starke, Genevieve M.; Meneveau, Charles; King, Jennifer; Gayme, Dennice F.

doi:10.1063/5.0042573

Cited by 11 publications

(12 citation statements)

References 30 publications

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“…This approach agrees well with large eddy simulations (LES) and field observations and has been extended to general wind farm layouts (Starke et al. 2021).…”

Section: Introductionsupporting

confidence: 79%

“…The coupled wake boundary layer (CWBL) model (Stevens, Gayme & Meneveau 2016) widens the applicability of coupled models by introducing a two-way coupling between a wake model and a top-down model. This approach agrees well with large eddy simulations (LES) and field observations and has been extended to general wind farm layouts (Starke et al 2021).…”

Section: Introductionsupporting

confidence: 77%

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Understanding wind farm power densities

Stevens

2023

J. Fluid Mech.

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Kirby et al. (J. Fluid Mech., vol. 953, 2022, A39) adapted the two-scale momentum theory (Nishino & Dunstan, J. Fluid Mech., vol. 894, A2) to large finite-sized farms. They demonstrated that analytical estimates agree excellently with large eddy simulations, and that the model provides a good upper limit of the power production for a given array density. Crucially, they introduced the concepts of farm-scale losses, caused by the atmospheric response to the whole farm, and turbine-scale losses, owing to internal flow interactions in the wind farm. These two new theoretical concepts offer a novel way to analyse the performance of extended wind farms. For large offshore wind farms, losses at the wind-farm scale are typically twice as high as at the turbine scale. This demonstrates that there is limited potential for layout optimizations of extended arrays. Instead, optimization strategies should focus on developing methods to increase the energy entrainment into the wind farm. This work provides an exciting roadmap for analysing the effective efficiency of large wind farms.

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“…This approach agrees well with large eddy simulations (LES) and field observations and has been extended to general wind farm layouts (Starke et al. 2021).…”

Section: Introductionsupporting

confidence: 79%

Section: Introductionsupporting

confidence: 77%

Understanding wind farm power densities

Stevens

2023

J. Fluid Mech.

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“…The parameter c ft (also a function of position) can be evaluated by averaging the wind farm thrust coefficient per unit area c ft upwind with respect to location x and along a streamline through the point of interest, assumed in the present study to be rectilinear. Following Starke et al (2021), we argue that such an averaging procedure better represents the fact that the IBL height at any x depends on the thrust coefficient per unit area experienced up to that point rather than on its local value. In order to perform the averaging operation, c ft is defined at every cell of a two-dimensional Cartesian sampling grid as…”

Section: Wind Farm Parametrizationmentioning

confidence: 99%

A shear stress parametrization for arbitrary wind farms in conventionally neutral boundary layers

Stipa,

Allaerts,

Brinkerhoff

2024

J. Fluid Mech.

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In the context of large off-shore wind farms, power production is influenced greatly by the turbine array's interaction with the atmospheric boundary layer. One of the most influencing manifestations of such complex interaction is the increased level of shear stress observed within the farm. This leads to higher momentum fluxes that affect the wind speed at the turbine locations and in the cluster wake. At the wind farm entrance, an internal boundary layer (IBL) grows due to the change in effective roughness imposed by the wind turbines, and for large enough clusters, this can reach the unperturbed boundary layer height in what is referred to as the fully developed regime. Downwind, a second IBL starts growing, while the shear stress profile decays exponentially to its unperturbed state. In the present study, we propose a simple analytical model for the vertical profile of the horizontal shear stress components in the three regions identified above. The model builds upon the top-down model of Meneveau (J. Turbul., vol. 13, 2012, N7), and assumes that the flow develops in a conventionally neutral boundary layer. The proposed parametrization is verified successfully against large-eddy simulations, demonstrating its ability to capture the vertical profile of horizontal shear stress, and its evolution both inside and downwind of the wind farm. Our findings suggest that the developed model can prove extremely useful to enhance the physical grounds on which new classes of coupled wind farm engineering models are based, leading to a better estimation of meso-scale phenomena affecting the power production of large turbine arrays.

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“…To capture this two-way interaction, it has been proposed to couple wake and top-down models; for example, by adjusting parameters in both models to match the hub-height-averaged velocities (Stevens, Gayme & Meneveau 2016 b ; Starke et al. 2021). Examples of two-way coupling can also be found in existing engineering software, e.g.…”

Section: Introductionmentioning

confidence: 99%

Two-scale interaction of wake and blockage effects in large wind farms

2022

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Turbine wake and farm blockage effects may significantly impact the power produced by large wind farms. In this study, we perform large-eddy simulations (LES) of 50 infinitely large offshore wind farms with different turbine layouts and wind directions. The LES results are combined with the two-scale momentum theory (Nishino & Dunstan, J. Fluid Mech., vol. 894, 2020, p. A2) to investigate the aerodynamic performance of large but finite-sized farms as well. The power of infinitely large farms is found to be a strong function of the array density, whereas the power of large finite-sized farms depends on both the array density and turbine layout. An analytical model derived from the two-scale momentum theory predicts the impact of array density very well for all 50 farms investigated and can therefore be used as an upper limit to farm performance. We also propose a new method to quantify turbine-scale losses (due to turbine–wake interactions) and farm-scale losses (due to the reduction of farm-average wind speed). They both depend on the strength of atmospheric response to the farm, and our results suggest that, for large offshore wind farms, the farm-scale losses are typically more than twice as large as the turbine-scale losses. This is found to be due to a two-scale interaction between turbine wake and farm induction effects, explaining why the impact of turbine layout on farm power varies with the strength of atmospheric response.

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The area localized coupled model for analytical mean flow prediction in arbitrary wind farm geometries

Cited by 11 publications

References 30 publications

Understanding wind farm power densities

Understanding wind farm power densities

A shear stress parametrization for arbitrary wind farms in conventionally neutral boundary layers

Two-scale interaction of wake and blockage effects in large wind farms

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