Energy Effectiveness of Arbitrary Arrays of Wind Turbines

Abstract

Determination of power degradation due to interference between wind turbines in an array is of importance in the engineering and economic planning of wind farms. A computer model for an arbitrary array of turbines is described. The basic fluid mechanics are treated in a simple but rational way. The turbine wake expands downstream due to ambient turbulence and mechanically generated turbulence (caused by momentum gradients) and entrains momentum and mass. Drag or momentum deficit, though, is conserved. Ground effect is handled by imaging. The effect of ambient turbulence is shown to be much greater than of that due to the momentum deficit generated by the turbine. The basic equations use fundamental fluid mechanical expressions related to drag conservation and wake growth due to turbulent entrainment and a family of self-similar wake profiles derived from experiment. This approach fully defines the wake velocity field. The wake of each turbine is then determined, subject to all upstream interferences. Power outputs of selected arrays as functions of wind direction are presented. The model is very well supported by the limited data available, and has proven effective and easy to implement. Advanced models incorporating nonuniformities in wind and turbulence and tower shadow are also described.