No abstract

Kinetic-energy transport and turbulence production within the shear layer of a horizontal-axis wind-turbine wake are investigated with respect to their influence on the tip-vortex pairwise instability, the so-called leapfrogging instability. The study quantifies the effect of near-wake instability and tip-vortex breakdown on the process of mean-flow kinetic-energy transport within the far wake of the wind turbine, in turn affecting the wake re-energising process. Experiments are conducted in an open-jet wind tunnel with a wind-turbine model of 60 cm diameter at a diameter-based Reynolds number range Re D = 150 000-230 000. The velocity fields in meridian planes encompassing a large portion of the wake past the rotor are measured both in the unconditioned and the phase-locked mode by means of stereoscopic particle image velocimetry. The detailed topology and development of the tip-vortex interactions are discussed prior to a statistical analysis based on the triple decomposition of the turbulent flow fields. The study emphasises the role of the pairing instability as a precursor to the onset of three-dimensional vortex distortion and breakdown, leading to increased turbulent mixing and kinetic-energy transport across the shear layer. Quadrant analysis further elucidates the role of sweep and ejection events within the two identified mixing regimes. Prior to the onset of the instability, vortices shed from the blade appear to inhibit turbulent mixing of the expanding wake. The second region is dominated by the leapfrogging instability, with a sudden increase of the net entrainment of kinetic energy. Downstream of the latter, random turbulent motion characterises the flow, with a significant increase of turbulent kinetic-energy production. In this scenario, the leapfrogging mechanism is recognised as the triggering event that accelerates the onset of efficient turbulent mixing followed by the beginning of the wake re-energising process.

The actuator disc is the oldest representation of a rotor, screw or propeller. Performance prediction is possible by applying momentum theory, giving integrated values for power and velocity. Computational fluid dynamics has provided much more flow details, but a full potential flow solution zooming in on these flow details was still absent. With the wake boundary discretized by vortex rings, flow states for energy extracting discs have been obtained for thrust coefficients up to 0.998. Boundary conditions are met with an accuracy of a few . Results from momentum theory are confirmed.Most rotor design codes use momentum theory in annulus or differential form, assuming that the axial velocity v x at the disc is uniform. However, the absolute velocity jvj is found to be uniform, and arguments for this are presented. The non-uniformity of v x is an inherent part of the flow solution caused by, in terms of momentum theory, the pressure acting at the annuli. This makes the annuli not independent from each other as assumed in current design codes. Although this was already known, it is now confirmed up to the highest thrust coefficients.Optimizing a rotor design should be carried out for the non-uniform distribution of v x . To enable this, an equation for the non-uniformity as function of thrust and radial position is presented, being a surface-fit to the calculated data. Qualitatively, the non-uniform distribution does the same as the Prandtl-Glauert-Shen tip correction applied to a uniform distribution.

The actuator disc (AD) model is commonly used to simplify the simulation of horizontal-axis wind-turbine aerodynamics. The limitations of this approach in reproducing the wake losses in wind farm simulations have been proven by a previous research. The present study is aimed at providing an experimental analysis of the near-wake turbulent flow of a wind turbine (WT) and a porous disc, emulating the actuator disc numerical model. The general purpose is to highlight the similarities and to quantify the differences of the two models in the near-wake region, characterised by the largest discrepancies. The velocity fields in the wake of a wind turbine model and a porous disc (emulation of the actuator disc numerical model) have been measured in a wind tunnel using stereo particle image velocimetry. The study has been conducted at low turbulence intensity in order to separate the problems of the flow mixing caused by the external turbulence and the one caused by the turbulence induced directly by the AD or the WT presence. The analysis, as such, showed the intrinsic differences and similarities between the flows in the two wakes, solely due to the wake-induced flow, with no influence of external flow fluctuations. The data analysis provided the time-average three-component velocity and turbulence intensity fields, pressure fields, rotor and disc loading, vorticity fields, stagnation enthalpy distribution, and mean-flow kinetic-energy fluxes in the shear layer at the border of the wake. The properties have been compared in the wakes of the two models. Even in the absence of turbulence, the results show a good match in the thrust and energy coefficient, velocity, pressure, and enthalpy fields between wind turbine and actuator disc. However, the results show a different turbulence intensity and turbulent mixing. The results suggest the possibility to extend the use of the actuator disc model in numerical simulation until the very near wake, provided that the turbulent mixing is correctly represented.

No abstract