Interaction between low-level jets and wind farms in a stable atmospheric boundary layer

Abstract

Low-level jets (LLJs) are the wind maxima in the lower regions of the atmosphere with a high wind energy potential. Here we use large-eddy simulations to study the effect of LLJ height on the flow dynamics in a wind farm with 10 × 4 turbines. We change the LLJ height and atmospheric thermal stratification by varying the surface cooling rate. We find that the first row power production is higher in the presence of a LLJ compared to a neutral reference case without LLJ. Besides, we show that the first row power production increases with decreasing LLJ height. Due to the higher turbulence intensity, the wind turbine wakes recover faster in a neutral boundary layer than in a stably stratified one. However, for strong thermal stratification with a low-height LLJ, the wake recovery can be faster than for the neutral reference case as energy can be entrained from the LLJ. Flow visualizations reveal that under stable stratification the growth of wind farm's internal boundary layer is restricted and the wind flows around the wind farm. Wind farms extract energy from LLJs through wake meandering and turbulent entrainment depending on the LLJ height. Both effects are advantageous for wake recovery, which is beneficial for the performance of downwind turbines. This finding is confirmed by an energy budget analysis, which reveals a significant increase in the kinetic energy flux in the presence of a LLJ. The jet strength reduces as it passes through consecutive turbine rows. For strong stratification, the combined effect of buoyancy destruction and turbulence dissipation is larger than the turbulent entrainment. Therefore, the power production of turbines in the back of the wind farm is relatively low for strong atmospheric stratifications. We find that the pronounced wind veer in stably stratified boundary layers creates asymmetry in the available wind resource, which can only be studied in finite-size wind farm simulations. We emphasize that spanwise-infinite wind farm simulations may underpredict wind farm performance as the additional beneficial effect of LLJ cannot be observed.

Modelling wakes and blockage i large-scale wind farms

“…r u 2 `r v 2 is the filtered velocity magnitude at the first grid level, and θ s is the filtered potential temperature at the surface, which is reduced at a set cooling rate of C r in Kelvin per hour rK{hs. When C r " 0 K{h, a conventionally neutral ABL is generated which has been confirmed by Gadde et al [125], asserting that in this case, the surface heat flux q ˚is negligible. This method of establishing stable stratification by reducing the surface temperature at a constant rate versus being driven by a constant heat flux also yielded similar results for Kumar et al [144].…”

“…In the previous chapters, we considered a neutral ABL, so here we describe the modifications required to incorporate thermal stratification. The large eddy simulation code is based on the version developed by Albertson and Parlange [63,64] and has been further updated to successfully simulate wind farms in stably stratified ABLs [125,134,135]. The governing equations are as follows.…”

“…where r S ij " 1 2 pB j r u i `Bi r u j q represents the resolved strain rate tensor, ν T represents the turbulent eddy viscosity, C smag represents the Smagorinsky coefficient for the subgrid scale stresses, ν θ is the eddy heat diffusivity, D smag represents the Smagorinsky coefficient for the sub-grid scale heat flux, and | r S| " p2 r S ij r S ij q 1{2 . We use a tuning-free, scale-dependent anisotropic minimum dissipation model [125,[138][139][140] to calculate the Smagorinsky coefficient dynamically, which makes the model particularly suitable for inhomogeneous flows, such as the flow through a wind farm.…”

“…For instance, when C r " 1.0 K{h, the low-level jet would reside partially within the rotor-swept area of the turbines. Depending on the jet's position and strength, its high energy potential and shear play an important role in sustaining turbulence within the boundary layer, consequently impacting wind farm performance [125,149].…”

“…Therefore, a stable ABL commonly occurs at night or when warm air flows over a cold surface such as polar oceans. In this case, the cooler denser air near the surface is not prone to rise, which means there is less turbulent mixing and the depth of this layer is relatively shallower, typically between 100 ´500 m [125]. Generally, mixing in this boundary layer is generated by shear and destroyed by buoyancy and viscosity [83].…”