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The wake meandering characteristics of four different wind turbine designs with diameters ranging from a few centimetres (wind tunnel scale) to a hundred metres (utility scale) are investigated using large-eddy simulation with the turbine blades and nacelle parametrised using a new actuator surface model. Different velocity fields and meandering behaviours are observed at near-wake locations. At far-wake locations, on the other hand, the mean velocity deficit profiles begin to collapse when scaled by the centreline velocity deficit based on the incoming wind speed at turbine hub height, suggesting far-wake similarity across scales. The turbine-added turbulence kinetic energy profiles are shown to also nearly collapse with each other in the far wake when normalised using a velocity scale defined by the thrust on the turbine rotor. Moreover, we show that at far-wake locations, the simulated flow fields for all four turbine designs exhibit similar wake meandering characteristics in terms of (1) a Strouhal number independent of rotor designs of different sizes and (2) the distributions of wake meandering wavelengths and amplitudes when normalised by the rotor diameter and a length scale defined by the turbine thrust respectively.

The flows behind a model wind turbine under two different turbine operating regimes (Region 2 for turbine operating at optimal condition with the maximum power coefficient and 1.4 degrees of pitch angle, and Region 3 for turbine operating at sub-optimal condition with a lower power coefficient and 7 degrees of pitch angle) are investigated using wind tunnel experiments and large-eddy simulations (LES). Measurements from the model wind turbine experiment reveal that the power coefficient and turbine wake are affected by the operating regime. Simulations employing a new class of actuator surface methods which parameterize both the turbine blades and nacelle with and without a nacelle model are carried out for each operating condition to study the influence of the operating regime and nacelle on the formation of the hub vortex and wake meandering. Flow field statistics and energy spectra of the simulated wakes are in good agreement with the measurements. For simulations with a nacelle model, the mean flow field is composed of an outer wake, caused by energy extraction from the incoming wind by turbine blades, and an inner wake directly behind the nacelle, while for the simulations without a nacelle model, the central region of the wake is occupied by a jet. The simulations with the nacelle model reveal an unstable helical hub vortex expanding outwards towards the outer wake; while the simulations without a nacelle model show a stable and columnar hub vortex. Because of the different interactions of the inner region of the wake with the outer region of the wake, a region with higher turbulence intensity is observed in the tip shear layer for the simulation with a nacelle model. The hub vortex for the turbine operating in Region 3 remains in a tight helical spiral and intercepts the outer wake a few diameters further downstream than for the turbine operating in Region 2. Wake meandering, a low frequency large-scale motion of the wake, commences in the region of high turbulence intensity for all simulations with and without a nacelle model indicating that neither a nacelle model nor an unstable hub vortex is a necessary requirement for the existence of wake meandering. However, further analysis of the wake meandering and instantaneous flow field using a filtering technique and dynamic mode decomposition show that the unstable hub vortex energizes the wake meandering. The turbine operating regime affects the shape and expansion of the hub vortex altering the location of the onset of the wake meandering and wake meander oscillating intensity. Most importantly, the unstable hub vortex promotes a high amplitude energetic meandering which cannot be predicted without a nacelle model. arXiv:1802.03836v1 [physics.flu-dyn]