Analytical solution for the cumulative wake of yawed wind turbines

Abstract

This thesis sets out to improve the physical grounding and predictive accuracy of cumulative wake effect modelling within wind farms with yawed turbines. It derives an analytical solution for the lateral velocity field within a wind farm and compares its predictions to those of computational fluid dynamics.

A parametric study is performed using a Reynolds-averaged Navier-Stokes (RANS) solver with the k-ε-fP turbulence model, Joukowsky rotor-based actuator disc, and neutral log-law inflow within the PyWakeEllipSys framework to determine the effects of yaw angle, thrust coefficient, and turbulence intensity on the lateral wake.

The results of this parametric study are used to solve an approximate form of conservation of mass and momentum in the lateral direction for a turbine within a wind farm. The solution is an explicit equation predicting the lateral velocity distribution and lateral wake deflection within a wind farm of arbitrary layout and with arbitrarily yawed turbines. It also provides a first mathematical proof of secondary wake steering.

The solution is implemented in Python and used to predict the velocity distributions in several wind farm cases, including for a single turbine, a two-turbine arrangement, and two wind farm cases with aligned and staggered layouts. These predictions are then compared against those of the RANS setup. The model significantly overestimates wake deflections unless corrected to neglect the near wake, but the corrected version shows promise, particularly in predicting wind farm power of the staggered layout, where the prediction is 19% closer to the RANS result than the prediction that considers lateral velocities equal to zero.