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

Li, Chao; Liu, Luoqin; Lu, Xi‐Yun; Stevens, Richard J. A. M.

doi:10.1017/jfm.2022.732

Cited by 5 publications

(4 citation statements)

References 64 publications

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“…Recent developments in this class of models include combining them with turbine wake models (Stevens, Gayme & Meneveau 2015, 2016 b ) or incorporating atmospheric (Emeis 2010; Abkar & Porté-Agel 2013; Peña & Rathmann 2014; Antonini & Caldeira 2021 a ; Li et al. 2022) and entrance effects (Meneveau 2012; Yang & Sotiropoulos 2016).…”

Section: Introductionmentioning

confidence: 99%

“…Building on the above assumptions, a 'top-down' class of models has been devised, which assume that the wind farm acts as an additional roughness element (Frandsen 1992;Emeis & Frandsen 1993;Calaf et al 2010). Recent developments in this class of models include combining them with turbine wake models (Stevens, Gayme & Meneveau 2015, 2016b or incorporating atmospheric (Emeis 2010;Abkar & Porté-Agel 2013;Peña & Rathmann 2014;Antonini & Caldeira 2021a;Li et al 2022) and entrance effects (Meneveau 2012;Yang & Sotiropoulos 2016).…”

Section: Introductionmentioning

confidence: 99%

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Turbulent entrainment in finite-length wind farms

2023

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In this article, we present an entrainment-based model for predicting the flow and power output of finite-length wind farms. The model is an extension of the three-layer approach of Luzzatto-Fegiz & Caulfield (Phys. Rev. Fluids, vol. 3, 2018, 093802) for wind farms of infinite length, and assumes dependence of key flow quantities, such as the wind farm bulk velocity, on the streamwise distance from the farm entrance. To assist our analysis and validate the proposed model, we undertake a series of large-eddy simulations with different turbine spacing arrangements and layouts. Comparisons are also made with the top-down model with entrance effects of Meneveau (J. Turbul., vol. 13, 2012, N7) and data from the literature. The finite-length entrainment model is shown to be capable of capturing the power drop between contiguous rows of turbines as well as describing the advection and turbulent transport of kinetic energy in both the entrance and fully developed regions. The fully developed regime is approximated only deep in the wind farm, after approximately 15 rows of turbines. Our data suggest that for the cases considered in this study, the empirical coefficients that can be used to describe turbulent entrainment and transfers above the wind farm exhibit little dependence on the farm layout and may be considered constant for modelling purposes. However, the flow field within the wind farm layer can be strongly modulated by the turbine density (spacing) as well as the array layout, and to that extent it can be argued that they are both primary factors determining the wind farm power output.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Turbulent entrainment in finite-length wind farms

2023

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“…Calaf, Meneveau & Meyers (2010) developed an improved top-down model by including an additional wake layer with enhanced turbulence levels. Later works have extended this approach to finite-length wind farms (Meneveau 2012), and included atmospheric stratification effects (Abkar & Porté-Agel 2013;Peña & Rathmann 2014;Sescu & Meneveau 2015;Li et al 2022). Although top-down models include the response of an idealised ABL to a large wind farm, this approach cannot account for layout effects.…”

Section: Introductionmentioning

confidence: 99%

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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“…Hezaveh et al [4] showed that "the wind-farm design with staggered-triangle clusters is the optimal design in terms of cost per unit power produced." Li et al [5] showed that the power output is higher in the staggered wind farms (horizontal-axis wind turbines) than in the aligned ones.…”

Section: Introductionmentioning

confidence: 99%

Wind-Tunnel Experiments on the Interactions among a Pair/Trio of Closely Spaced Vertical-Axis Wind Turbines

Jodai

Hara

2023

Energies

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To elucidate the wind-direction dependence of the rotor performance in closely spaced vertical-axis wind turbines, wind-tunnel experiments were performed at a uniform wind velocity. In the experiments, a pair/trio of three-dimensional printed model turbines with a diameter of D = 50 mm was used. The experiments were performed systematically by applying incremental adjustments to the rotor gap g and rotational direction of each rotor and by changing the wind direction. For tandem layouts, the rotational speed of the downwind rotor is 75–80% that of an isolated rotor, even at g/D = 10. For the average rotational speed of the rotor pair, an origin-symmetrical and a line-symmetrical distribution are observed in the co-rotating and inverse-rotating configurations, respectively, thereby demonstrating the wind-direction dependence for the rotor pair. The inverse-rotating trio configuration yields a higher average rotational speed than the co-rotating trio configuration for any rotor spacing under the ideal bidirectional wind conditions. The maximum average rotational speed should be obtained for a wind direction of θ = 0° in the inverse-rotating trio configuration. The wind-direction dependence of the rotational speeds of the three turbines was explained via flow visualization using a smoke-wire method and velocity field study using two-dimensional computational fluid dynamics.

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

Cited by 5 publications

References 64 publications

Turbulent entrainment in finite-length wind farms

Turbulent entrainment in finite-length wind farms

Understanding wind farm power densities

Wind-Tunnel Experiments on the Interactions among a Pair/Trio of Closely Spaced Vertical-Axis Wind Turbines

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