Wind Turbine Performance in Very Large Wind Farms: Betz Analysis Revisited

West, Jacob; Lele, Sanjiva K.

doi:10.3390/en13051078

Cited by 11 publications

(7 citation statements)

References 40 publications

(68 reference statements)

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“…With this assumption, we hypothetically divide the flow field into two types of zones; namely the inviscid flow zones, which are analysed using the LMADT neglecting the effect of viscous (or turbulent) mixing, and the viscous flow zones, which are modelled separately to account for the effect of mixing. This approach is also in line with the results of a recent LES study of flow past a periodic array of actuator discs (West & Lele 2020) showing that the effects of inviscid and viscous (turbulent) flow processes are dominant, respectively, in the vicinity of the turbines and in the rest of the flow field.…”

Section: Invsupporting

confidence: 86%

Performance and wake characteristics of tidal turbines in an infinitely large array

Ouro

Nishino

2021

J. Fluid Mech.

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The efficiency of tidal stream turbines in a large array depends on the balance between negative effects of turbine-wake interactions and positive effects of bypass-flow acceleration due to local blockage, both of which are functions of the layout of turbines. In this study we investigate the hydrodynamics of turbines in an infinitely large array with aligned or staggered layouts for a range of streamwise and lateral turbine spacing. First, we present a theoretical analysis based on an extension of the linear momentum actuator disc theory for perfectly aligned and staggered layouts, employing a hybrid inviscid-viscous approach to account for the local blockage effect within each row of turbines and the viscous (turbulent) wake mixing behind each row in a coupled manner. We then perform large-eddy simulation (LES) of open-channel flow for 28 layouts of tidal turbines using an actuator line method with doubly periodic boundary conditions. Both theoretical and LES results show that the efficiency of turbines (or the power of turbines for a given bulk velocity) in an aligned array decreases as we reduce the streamwise turbine spacing, whereas that in a staggered array remains high and may even increase due to the positive local blockage effect (causing the local flow velocity upstream of each turbine to exceed the bulk velocity) if the lateral turbine spacing is sufficiently small. The LES results further reveal that the amplitude of wake meandering tends to decrease as we reduce the lateral turbine spacing, which leads to a lower wake recovery rate in the near-wake region. These results will help to understand and improve the efficiency of tidal turbines in future large arrays, even though the performance of real tidal arrays may depend not only on turbine-to-turbine interactions within the array but also on macro-scale interactions between the array and natural tidal currents, the latter of which are outside the scope of this study.

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Section: Invsupporting

confidence: 86%

Performance and wake characteristics of tidal turbines in an infinitely large array

Ouro

Nishino

2021

J. Fluid Mech.

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“…As illustrated earlier in figure 1, this approach treats the region around the turbine as an inviscid flow region which is modelled with LMADT, followed by a viscous mixing zone downstream which is modelled separately. This approach is in line with the results of West & Lele (2020) who, in a large-eddy simulation study of flow around an actuator disc, showed that inviscid flow processes dominate around the turbine and viscous processes dominate further downstream. We adopt the same simplification in this analysis as in Ouro & Nishino (2021) that mixing takes place uniformly across the viscous mixing zone and will be defined by a single parameter such that , where is a streamtubes velocity entering the viscous mixing zone, is the average velocity across the whole domain and is the velocity as it exits the viscous mixing zone.…”

Section: Multi-row Resultssupporting

confidence: 90%

Single and multi-row turbine performance in bounded shear flow

Juniper

Nishino

2023

J. Fluid Mech.

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Predicting the performance of large turbine arrays requires the understanding of many physical factors, such as array geometry, turbine operation, inflow conditions and turbulent wake mixing. Due to the large parameter space that an array may be optimised over, low-order models with low computational cost are often employed. This paper extends one of these models, the inviscid–viscous coupled model, for multi-row turbine modelling. Firstly, an extension to the inviscid actuator disc theory is presented by removing the limit on the number of discrete streamtubes computed. The extended model allows for the quantification of the impact of shear in the bypass and core flows separately. In particular, it is shown that averaging a sheared bypass flow profile can result in a substantial over-prediction of the power of a turbine in a laterally bounded flow as the effective blockage of the flow increases. The model is also used to confirm that an approximation using a limited number of streamtubes in some previous applications of the inviscid–viscous approach has a negligible impact on the results. Secondly, we explore the performance of a multi-row array with either uniform or varying turbine resistance across different rows. Results suggest that by varying resistance across rows, the array may outperform the uniform resistance case. The performance gain is dependent, however, on the arrangement and inter-turbine spacing both in the spanwise and streamwise directions.

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“…Hence, by calculating C P for a range of α between 0 and 1, we can find the maximum power coefficient, C Pmax , for a given set of λ/C f 0 , γ and ζ as shown earlier in Figure 1. Note that the exact value of γ is unknown without solving the internal sub-problem for a given wind farm; however, γ = 2 is deemed a good approximation for the prediction of upper limits of power production [13,15]. It is also worth noting that the aforementioned simple theoretical prediction of the upper limit by Miller et al [7] can be reproduced by the present model with λ/C f 0 → ∞, γ = 2 and ζ = 0 (corresponding to an infinitely large and dense wind farm; see [16] for further details).…”

Section: =mentioning

confidence: 99%

Time-Dependent Upper Limits to the Performance of Large Wind Farms Due to Mesoscale Atmospheric Response

2021

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A prototype of a new physics-based wind resource assessment method is presented, which allows the prediction of upper limits to the performance of large wind farms (including the power loss due to wind farm blockage) in a site-specific and time-dependent manner. The new method combines the two-scale momentum theory with a numerical weather prediction (NWP) model to assess the “extractability” of wind, i.e., how high the wind speed at a given site can be maintained as we increase the number of turbines installed. The new method is applied to an offshore wind farm site in the North Sea to demonstrate that: (1) Only a pair of NWP simulations (one without wind farm and the other with wind farm with an arbitrary level of flow resistance) are required to predict the extractability. (2) The extractability varies significantly from time to time, which may cause more than 30% of change in the upper limit of the performance of medium-to-high-density offshore wind farms. These results suggest the importance of considering not only the natural wind speed but also its extractability in the prediction of (both long- and short-term) power production of large wind farms.

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Wind Turbine Performance in Very Large Wind Farms: Betz Analysis Revisited

Cited by 11 publications

References 40 publications

Performance and wake characteristics of tidal turbines in an infinitely large array

Performance and wake characteristics of tidal turbines in an infinitely large array

Single and multi-row turbine performance in bounded shear flow

Time-Dependent Upper Limits to the Performance of Large Wind Farms Due to Mesoscale Atmospheric Response

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