An unsteady vortex lattice method model of a horizontal axis wind turbine operating in an upstream rotor wake

An unsteady formulation of the vortex lattice method, VLM, is presented that uses a force- free representation of the wake behind a horizontal axis wind turbine, HAWT, to calculate the aerodynamic loading on a turbine operating in the wake of an upstream rotor. A Cartesian velocity grid is superimposed over the computational domain to facilitate the representation of the atmospheric turbulence surrounding the turbine and wind shear. The wake of an upstream rotor is modelled using two methods: a mean velocity deficit with superimposed turbulence, based on experimental observations, and a purely numeric periodic boundary condition. Both methods are treated as frozen and propagated with the velocity grid. Measurements of the mean thrust and blade root bending moment on a three bladed horizontal axis rotor modelling a 5 MW HAWT at 1:250 scale were carried out in a wind tunnel. Comparisons are made between operation in uniform flow and in the wake of a similarly loaded rotor approximately 6.5 diameters upstream. The measurements were used to validate the output from the VLM simulations, assuming a completely rigid rotor. The trends in the simulation thrust predictions are found to compare well with the uniform flow case, except at low tip speed ratios where there are losses due to stall which are yet to be included in the model. The simple wake model predicts the mean deficit, whilst the periodic boundary condition captures more of the frequency content of the loading in an upstream wake. However, all the thrust loads are over-predicted. The simulation results severely overestimate the bending moment, which needs addressing. However, the reduction in bending due to the simple wake model is found to reflect the experimental data reasonably well.