Self-similarity and flow characteristics of vertical-axis wind turbine wakes: an LES study

Large eddy simulation (LES) is coupled with a turbine model to study the structure of the wake behind a vertical-axis wind turbine (VAWT). In the simulations, a tuning-free anisotropic minimum dissipation model is used to parameterise the subfilter stress tensor, while the turbine-induced forces are modelled with an actuator line technique. The LES framework is first validated in the simulation of the wake behind a model straight-bladed VAWT placed in the water channel and then used to study the wake structure downwind of a full-scale VAWT sited in the atmospheric boundary layer. In particular, the self-similarity of the wake is examined, and it is found that the wake velocity deficit can be well characterised by a two-dimensional multivariate Gaussian distribution. By assuming a self-similar Gaussian distribution of the velocity deficit, and applying mass and momentum conservation, an analytical model is developed and tested to predict the maximum velocity deficit downwind of the turbine. Also, a simple parameterisation of VAWTs for LES with very coarse grid resolutions is proposed, in which the turbine is modelled as a rectangular porous plate with the same thrust coefficient. The simulation results show that, after some downwind distance (x/D ≈ 6), both actuator line and rectangular porous plate models have similar predictions for the mean velocity deficit. These results are of particular importance in simulations of large wind farms where, due to the coarse spatial resolution, the flow around individual VAWTs is not resolved.