Large-Eddy Simulation of an Extended Wind Farm Using PALM Model System: Wake Dynamics and Power Output

Large-eddy simulation (LES) of wind farms is often limited by the computational cost required to represent many turbine rows and to obtain statistically converged wake and power statistics. Here, we present LES of an extended wind-farm configuration using the PALM model system, where cyclic lateral boundary conditions are employed to emulate interior-farm interaction in an idealized neutral boundary layer. The setup consists of nine identical horizontal-axis wind turbines arranged in a staggered array within the computational domain. Time-averaged hub-height fields show coherent wake corridors with a mean inflow-speed reduction of $23.7$ % (array-mean across turbines) relative to an undisturbed background wind speed, and peak wake deficits reaching $71.4$ % in the near-wake region. Turbulence levels increase markedly in the wake shear layers, with hub-height turbulence intensity enhanced by $32.2$ % in the rotor region compared to background conditions; correspondingly, the peak hub-height SGS-TKE increases by a factor of 6.74 relative to background. Vertically averaged profiles indicate a momentum deficit within the turbine layer and gradual recovery aloft; the streamwise turbulent momentum flux remains predominantly negative, demonstrating the downward transport of higher-momentum air from above as a key recovery mechanism. Turbine rotor-power statistics show an initial adjustment followed by a quasi-stationary regime, with a farm-mean rotor power of $1.93$ MW and persistent inter-turbine variability characterized by a mean coefficient of variation of $61.2$ %. Overall, the results demonstrate that the proposed extended-farm LES approach enables computationally efficient quantification of wake dynamics, vertical momentum transport, and their impact on power variability under idealized neutral wind-farm conditions.