Richard J.A.M. Stevens

Physics of Fluids

University of Twente

Large eddy simulations of wind-farms

Similar to other renewable energy sources, wind energy is characterized by a low power density. Large onshore and offshore wind farms, consisting of arrays of ever larger wind turbines, are being envisioned and built to make a considerable contribution to the world’s energy supply. These wind turbines interact with the environment over a wide range of length scales, from millimeters (viscous scales) and meters (wakes and tip vortices) to hundreds of meters (interturbine spacing) and kilometers (wind farms). This large scale separation makes the analysis and design of wind farms challenging from both theoretical and numerical perspectives. A detailed understanding of the relevant physics is critical for efficient wind-farm designs. High-fidelity simulations allow the conditions under which wind-farm performance is tested to be specified fully and therefore provide insight into the complex interactions that dictate this performance.

In this project, we use large-eddy simulations to develop physics-based models for predicting the performance of very large wind farms; see also modeling of wind-farm performance. Movie 1 shows a three-dimensional visualization of a large-eddy simulation (LES) capturing the interaction between the atmosphere and a very large aligned wind farm; see Ref. 3 and the corresponding press releases by AIP and FOM. The movie shows the turbulent wakes created behind the turbines and how these wakes begin to interact farther downstream. White particles released periodically at the wind-farm entrance disperse rapidly and reveal the strongly turbulent nature of the flow. Figure 1 shows the power output as a function of downstream position for several wind-farm configurations. In the fully developed region, the power output becomes approximately constant, as shown in figures 1c and 1d. Here, the wind-farm dynamics are dominated by interacting turbine wakes but are also influenced by the atmospheric flow above the farm. We have investigated, for example, the effect of turbine density on the performance of very large wind farms [7] and the effect of wind-farm size on the optimal turbine spacing [6]. Our recent featured energy-budget analysis shows how recovery shifts from lateral transport behind one turbine to vertical transport and downward mean flow behind larger wind farms.

Illustrated main finding

The paper separates wind-farm power loss into a turbine-scale component from interactions within the array and a farm-scale component from the atmospheric boundary layer's response to aggregate drag. This conceptual split clarifies why layout optimization cannot remove the whole-farm momentum-supply limit.

See the two-scale loss schematic and evidence boundaries.

Movie 1. Three-dimensional visualization of the flow field in a simulated wind farm. The blue regions indicate low-velocity turbine wakes. Visualization by David Bock using XSEDE (Extreme Science and Engineering Discovery Environment).

Sketches of aligned and staggered wind-farm turbine layouts and power output versus downstream position

Figure 1. (a,b) Sketches of aligned and staggered wind farms. The sketches define the streamwise Sx and spanwise Sy turbine spacings, which are normalized by the turbine diameter D. Panel (b) also defines the alignment angle Ψ=arctan(Sdy/Sx) with respect to the incoming wind direction, where Sdy is the spanwise offset between successive turbine rows. (c) Power output as a function of downstream position for Sx=7.85 and Sy=5.24 and different Ψ. (d) Determination of the power output in the fully developed region (P∞/P1) for the aligned and staggered configurations.

References

  1. R.J.A.M. Stevens, C. Meneveau,
    Flow Structure and Turbulence in Wind Farms,
    Annual Review of Fluid Mechanics, 49, 311-339 (2017).
  2. A. Stieren, R.J.A.M. Stevens,
    Impact of wind farm wakes on flow structures in and around downstream wind farms,
    Flow 2, E21 (2022). Illustrated main finding
  3. J.M.I. Strickland, R.J.A.M. Stevens,
    Effect of thrust coefficient on the flow blockage effects in closely-spaced spanwise-infinite turbine arrays,
    J. Phys. Conf. Ser. 1618, 062069 (2020). Illustrated main finding
  4. M. Zhang, M.G. Arendshorst, R.J.A.M. Stevens,
    Large eddy simulations of the effect of vertical staggering in large wind farms,
    Wind Energy 22 (2), 189-204 (2019). Illustrated main finding
  5. L.J. Lukassen, R.J.A.M. Stevens, C. Meneveau, M. Wilczek,
    Modeling space-time correlations of velocity fluctuations in wind farms,
    Wind Energy 21 (7), 474-487 (2018).
  6. M. Zhang, R.J.A.M. Stevens,
    Exploring a better turbine layout in vertically staggered wind farms,
    J. Phys. Conf. Ser. 1037, 072041 (2018)
  7. M. Zhang, R.J.A.M. Stevens,
    Characterizing the coherent structures in large eddy simulations of aligned windfarms,
    J. Phys.: Conf. Ser. 854, 012052 (2017).
  8. R.J.A.M. Stevens, L.A. Martínez Tossas, C. Meneveau,
    Comparison of wind farm large eddy simulations using actuator disk and actuator line models with wind tunnel experiments,
    Renewable Energy, 116 (A), 470-478 (2018). Illustrated main finding
  9. R.J.A.M. Stevens, D.F. Gayme, C. Meneveau,
    Effects of turbine spacing on the power output of extended wind-farms,
    Wind Energy 19 (2), 359-370 (2016).
  10. R.J.A.M. Stevens,
    Dependence of optimal wind-turbine spacing on wind-farm length,
    Wind Energy 19 (4), 651-663 (2016).
  11. L.E.M. Lignarolo, D. Mehta, R.J.A.M. Stevens, A.E. Yilmaz, G. van Kuik, S.J. Andersen, C. Meneveau, C.J. Simão Ferreira, D. Ragni, J. Meyers, G.J.W. van Bussel, J. Holierhoek,
    Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine,
    Renewable Energy 94, 510-523 (2016).
  12. L.A. Martínez Tossas, R.J.A.M. Stevens, C. Meneveau,
    Wind Turbine Large-Eddy Simulations on Very Coarse Grid Resolutions using an Actuator Line Model,
    34th Wind Energy Symposium, AIAA SciTech, AIAA 2016-1261, 1-7 (2016).
  13. R.J.A.M. Stevens, D. F. Gayme, C. Meneveau,
    Large eddy simulation studies of the effects of alignment and wind farm length,
    J. of Renewable and Sustainable Energy 6, 023105 (2014),
    Highlighted by AIP News, April 1 2014,
    Featured by FOM News, April 3 2014.
    Featured by Johns Hopkins Mechanical Engineering news, April 2014.
  14. R.J.A.M. Stevens, C. Meneveau,
    Temporal structure of aggregate power fluctuations in large-eddy simulations of extended wind-farms,
    J. of Renewable and Sustainable Energy 6, 043102 (2014).
  15. R.J.A.M. Stevens, J. Graham, C. Meneveau,
    A concurrent precursor inflow method for Large Eddy Simulations and applications to finite length wind farms,
    Renewable Energy 68, 46-50 (2014).