Exploring a better turbine layout in vertically staggered wind farms

Vertical staggering of wind turbines can lead to an increased power production in the entrance region of a wind farm because downstream turbines are consequently outside the wakes of preceding turbines. We perform large eddy simulations of different vertically staggered wind farm configurations for which we keep the average turbine hub height the same. We find that the turbine power output in the entrance region of the wind farm is significantly higher when the first turbine row is elevated than when the first turbine row is lowered. The reason is that this allows the first high turbine row to fully benefit from the strong winds at a high elevation. In the fully developed region of the wind farm the power production of the vertically staggered wind farms is similar to the power production of the corresponding reference aligned wind farm, while the normalized power fluctuations can be significantly higher than in the reference wind farm

Effects of wind turbine rotor tilt on large-scale wind farms

Recent studies have explored the use of rotor tilt adjustments to reduce wake losses in wind farms. While downward wake deflection in aligned wind farms has shown promise for significant power gains, the impact of wind farm layout on the effectiveness of tilt strategies is not yet fully understood. Additionally, the effect on downstream farms remains unclear. Our large eddy simulations reveal that a rotor tilt of 20 degrees significantly reduces wake losses in aligned wind farms. For wind farms with 8 turbine rows, we observe an overall increase in wind farm productivity of up to 11%. However, tilting the rotors may decrease power production in staggered wind farms, where wake losses are inherently lower due to the increased spacing between turbines. Our findings also suggest that a downstream wind farm might benefit from an upstream farm implementing rotor tilt, although this advantage is primarily observed in the first row of the downstream farm

Effect of turbine alignment on the average power output of wind-farms

Using Large Eddy Simulation (LES), we investigate the influence of the alignment of successive turbine rows on the average power output of a finite length wind-farm with a stream-wise spacing between the turbines of Sx = 7:85D and a span-wise spacing of Sy = 5:23D, where D is the turbine diameter. Different turbine alignments affect the extent to which wakes from upstream turbines interact with downstream turbines. We consider 13 turbine rows in the stream-wise direction and change the layout of the wind-farm by adjusting the angle y = arctan Sdy Sx with respect to the incoming flow direction, where Sdy indicates the span-wise offset from one turbine row to the next. For the case considered here, y = 0 degrees corresponds to an aligned windfarm, while a perfectly staggered configuration occurs at y =arctan[(5:23D=2)=7:85D]=18:43 degrees. We simulate the interaction between each wind-farm and the atmospheric boundary layer using a LES that uses a newly developed concurrent-precursor inflow method. For an aligned configuration we observe a nearly constant average turbine power output for the second and subsequent turbine rows, which is about 60% of the average power produced by the turbines in the first row. With increasing y the power loss in subsequent turbine rows is more gradual. We find that the highest average power output is not obtained for a staggered wind-farm (y = 18:43 degrees), but for an intermediate alignment of around y = 12 degrees. Such an intermediate alignment allows more turbines to be outside the wake of upstream turbines than in the staggered configuration in which turbines are directly in the wake of turbines placed two rows upstream

The Mean Wind and Potential Temperature Flux Profiles in Convective Boundary Layers

We develop innovative analytical expressions for the mean wind and potential temperature flux profiles in convective boundary layers (CBLs). CBLs are frequently observed during daytime as the Earth's surface is warmed by solar radiation. Therefore, their modeling is relevant for weather forecasting, climate modeling, and wind energy applications. For CBLs in the convective-roll dominated regime, the mean velocity and potential temperature in the bulk region of the mixed layer are approximately uniform. We propose an analytical expression for the normalized potential temperature flux profile as a function of height, using a perturbation method approach in which we employ the horizontally homogeneous and quasi-stationary characteristics of the surface and inversion layers. The velocity profile in the mixed layer and the entrainment zone is constructed based on insights obtained from the proposed potential temperature flux profile and the convective logarithmic friction law. Combining this with the well-known Monin-Obukhov similarity theory allows us to capture the velocity profile over the entire boundary layer height. The proposed profiles agree excellently with large-eddy simulation results over the range of $-L/z_0 \in [3.6\times10^2, 0.7 \times 10^5]$, where $L$ is the Obukhov length and $z_0$ is the roughness length.Comment: 12 pages, 6 figure

Using the coupled wake boundary layer model to evaluate the effect of turbulence intensity on wind farm performance

We use the recently introduced coupled wake boundary layer (CWBL) model to predict the e ect of turbulence intensity on the performance of a wind farm. The CWBL model combines a standard wake model with a \top-down" approach to get improved predictions for the power output compared to a stand-alone wake model. Here we compare the CWBL model results for di erent turbulence intensities with the Horns Rev eld measurements by Hansen et al., Wind Energy 15, 183196 (2012). We show that the main trends as function of the turbulence intensity are captured very well by the model and discuss di erences between the eld measurements and model results based on comparisons with LES results from Wu and Port e-Agel, Renewable Energy 75, 945-955 (2015)

Numerical simulations of rotating Rayleigh-Bénard convection

The Rayleigh-Bénard (RB) system is relevant to astro- and geophysical phenomena, including convection in the ocean, the Earth’s outer core, and the outer layer of the Sun. The dimensionless heat transfer (the Nusselt number Nu) in the system depends on the Rayleigh number Ra=ßg¿L 3/(¿¿) and the Prandtl number Pr=¿/¿. Here, ß is the thermal expansion coefficient, g the gravitational acceleration, ¿ the temperature difference between the bottom and top, and ¿ and ¿ the kinematic viscosity and the thermal diffusivity, respectively. The rotation rate H is used in the form of the Rossby number Ro=(ßg¿/L)/(2H). The key question is: How does the heat transfer depend on rotation and the other two control parameters: Nu(Ra, Pr, Ro)? Here we will answer this question by giving a summary of our result