Analytical solution for the cumulative wake of wind turbines in wind farms

TL;DR

This paper presents an explicit analytical model for predicting wind farm wake effects based on conservation laws, validated with large-eddy simulations, offering improved understanding of flow distributions and wake interactions.

Contribution

It introduces a novel explicit analytical solution for wind farm wake prediction that does not rely on superposition techniques, validated against LES data.

Findings

The model accurately predicts flow distributions in moderate-sized wind farms.

A modified conservation of momentum deficit improves wake predictions at short and far distances.

The model reveals limitations of common wake superposition methods.

Abstract

This paper solves an approximate form of conservation of mass and momentum for a turbine in a wind farm array. The solution is a fairly simple explicit relationship that predicts the streamwise velocity distribution within a wind farm with an arbitrary layout. As this model is obtained by solving flow governing equations directly for a turbine that is subject to upwind turbine wakes, no ad hoc superposition technique is needed to predict wind farm flows. A suite of large-eddy simulations (LES) of wind farm arrays is used to examine self-similarity as well as validity of the so-called conservation of momentum deficit for turbine wakes in wind farms. The simulations are performed with and without the presence of some specific turbines in the wind farm. This allows us to systematically study some of the assumptions made to develop the analytical model. A modified version of the conservation of momentum deficit is also proposed to provide slightly better results at short downwind distances, as well as in the far wake of turbines deep inside a wind farm. Model predictions are validated against the LES data for turbines in both full-wake and partial-wake conditions. While our results highlight the limitation in capturing the flow speed-up between adjacent turbine columns, the model is overall able to acceptably predict flow distributions for a moderately sized wind farm. Finally, the paper employs the new model to provide insights on the accuracy of common wake superposition methods.