Optimal turbine spacing in fully developed wind farm boundary layers

Meyers, Johan; Meneveau, Charles

doi:10.1002/we.469

Cited by 306 publications

(242 citation statements)

References 19 publications

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“…10 and 11, where a thought experiment illustrated how considering only wind speeds and turbine specifications can yield generation rates that are physically unrealizable. The method is based on an analytical description of the momentum balance of the wind farm, a central concept used in similar studies on large-scale wind power limits (20)(21)(22) or for other forms of renewable energy such as tidal power (23,24) (detailed methodology is given in SI Appendix). It assumes that when wind farms extend tens of kilometers downwind, horizontal kinetic energy has either been extracted from the mean flow by the first few rows of turbines or has been lost to turbulent dissipation, so that the generation rate of wind turbines further downwind is then limited by the downward flux of kinetic energy.…”

Section: Methodsmentioning

confidence: 99%

Two methods for estimating limits to large-scale wind power generation

Miller

Brunsell

Mechem

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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Wind turbines remove kinetic energy from the atmospheric flow, which reduces wind speeds and limits generation rates of large wind farms. These interactions can be approximated using a vertical kinetic energy (VKE) flux method, which predicts that the maximum power generation potential is 26% of the instantaneous downward transport of kinetic energy using the preturbine climatology. We compare the energy flux method to the Weather Research and Forecasting (WRF) regional atmospheric model equipped with a wind turbine parameterization over a 10 5 km 2 region in the central United States. The WRF simulations yield a maximum generation of 1.1 W e ·m −2 , whereas the VKE method predicts the time series while underestimating the maximum generation rate by about 50%. Because VKE derives the generation limit from the preturbine climatology, potential changes in the vertical kinetic energy flux from the free atmosphere are not considered. Such changes are important at night when WRF estimates are about twice the VKE value because wind turbines interact with the decoupled nocturnal low-level jet in this region. Daytime estimates agree better to 20% because the wind turbines induce comparatively small changes to the downward kinetic energy flux. This combination of downward transport limits and wind speed reductions explains why large-scale wind power generation in windy regions is limited to about 1 W e ·m −2 , with VKE capturing this combination in a comparatively simple way.generation limits | turbine-atmosphere interactions | wind resource | kinetic energy flux | extraction limits W ind power has progressed from being a minor source of electricity to a technology that accounted for 3.3% of electricity generation in the United States and 2.9% globally in 2011 (1, 2). Combined with an increase in quantity, the average US wind turbine also changed from 2001 to 2012; hub height increased by 40%, rotor-swept area increased by 180%, and rated capacity increased by 100% (2). Likely a combination of both the above-noted technological innovations and improved siting, the per-turbine capacity factor, the ratio of the electricity generation rate (MW e ) to the rated capacity (MW i ), increased globally from 17% in 2001 to 29% in 2012 (1, 2), making a recently deployed wind farm likely to generate about 70% more electricity from the same installed capacity.Combining climate datasets with these observed trends of greater-rated capacities and capacity factors, several academic and government research studies estimate large-scale wind power electricity generation rates of up to 7 W e ·m −2 (3-7). However, a growing body of research suggests that as larger wind farms cover more of the Earth's surface, the limits of atmospheric kinetic energy generation, downward transport, and extraction by wind turbines limits large-scale electricity generation rates in windy regions to about 1.0 W e ·m −2 (8-14). Ideally, these inherent atmospheric limitations to generating electricity with wind power could be considered without scenario-and technol...

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Section: Methodsmentioning

confidence: 99%

Two methods for estimating limits to large-scale wind power generation

Miller

Brunsell

Mechem

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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“…For example, an optimization study utilizing Large Eddy Simulation (LES) has suggested the optimal spacing of HAWTs to be 15 D on the basis of minimizing costs per square rotor diameter. 4 More recently, a row-offset arrangement was demonstrated to allow for a greater wake recovery due to the increased streamwise spacing within the array. 5 Moreover, by decreasing the power output of upstream turbines, the performance of downstream turbines and the power output of the array as a whole can be increased.…”

Section: Introductionmentioning

confidence: 99%

Performance enhancement of downstream vertical-axis wind turbines

Brownstein

Kinzel

Dabiri

2016

Journal of Renewable and Sustainable Energy

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Numerical investigation of the yawed wake and its effects on the downstream wind turbine J. Renewable Sustainable Energy 8, 033303 (2016) Increased power production is observed in downstream vertical-axis wind turbines (VAWTs) when positioned offset from the wake of upstream turbines. This effect is found to exist in both laboratory and field environments with pairs of co-and counter-rotating turbines, respectively. It is hypothesized that the observed production enhancement is due to flow acceleration adjacent to the upstream turbine due to bluff body blockage, which would increase the incident freestream velocity on appropriately positioned downstream turbines. A low-order model combining potential flow and actuator disk theory captures this effect. Additional laboratory and field experiments further validate the predictive capabilities of the model. Finally, an evolutionary algorithm reveals patterns in optimized VAWT arrays with various numbers of turbines. A "truss-shaped" array is identified as a promising configuration to optimize energy extraction in VAWT wind farms by maximizing the performance enhancement of downstream turbines. Published by AIP Publishing.

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“…Recent extensive application of the actuator disc model in the numerical simulation of wind farms can be found in the works of Meyers and Meneveau (2012) and Calaf et al (2010). El Kasmi and Masson (2008) developed a modified k-e model for the actuator disc accounting for energy exchange between large and small scale turbulence structures in the region close to the disc.…”

mentioning

confidence: 99%

Experimental comparison of a wind-turbine and of an actuator-disc near wake

Lignarolo

Ragni

Ferreira

et al. 2016

Journal of Renewable and Sustainable Energy

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The actuator disc (AD) model is commonly used to simplify the simulation of horizontal-axis wind-turbine aerodynamics. The limitations of this approach in reproducing the wake losses in wind farm simulations have been proven by a previous research. The present study is aimed at providing an experimental analysis of the near-wake turbulent flow of a wind turbine (WT) and a porous disc, emulating the actuator disc numerical model. The general purpose is to highlight the similarities and to quantify the differences of the two models in the near-wake region, characterised by the largest discrepancies. The velocity fields in the wake of a wind turbine model and a porous disc (emulation of the actuator disc numerical model) have been measured in a wind tunnel using stereo particle image velocimetry. The study has been conducted at low turbulence intensity in order to separate the problems of the flow mixing caused by the external turbulence and the one caused by the turbulence induced directly by the AD or the WT presence. The analysis, as such, showed the intrinsic differences and similarities between the flows in the two wakes, solely due to the wake-induced flow, with no influence of external flow fluctuations. The data analysis provided the time-average three-component velocity and turbulence intensity fields, pressure fields, rotor and disc loading, vorticity fields, stagnation enthalpy distribution, and mean-flow kinetic-energy fluxes in the shear layer at the border of the wake. The properties have been compared in the wakes of the two models. Even in the absence of turbulence, the results show a good match in the thrust and energy coefficient, velocity, pressure, and enthalpy fields between wind turbine and actuator disc. However, the results show a different turbulence intensity and turbulent mixing. The results suggest the possibility to extend the use of the actuator disc model in numerical simulation until the very near wake, provided that the turbulent mixing is correctly represented.

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Optimal turbine spacing in fully developed wind farm boundary layers

Cited by 306 publications

References 19 publications

Two methods for estimating limits to large-scale wind power generation

Two methods for estimating limits to large-scale wind power generation

Performance enhancement of downstream vertical-axis wind turbines

Experimental comparison of a wind-turbine and of an actuator-disc near wake

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