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Register a new userA vortex sheet based analytical model of the curled wake behind yawed wind turbines
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Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.
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The fluid dynamics video considers an array of two NREL 5-MW turbines separated by seven rotor diameters in a neutral atmospheric boundary layer (ABL). The neutral atmospheric boundary-layer flow data were obtained from a precursor ABL simulation using a Large-Eddy Simulation (LES) framework within OpenFOAM. The mean wind speed at hub height is 8m/s, and the surface roughness is 0.2m. The actuator line method (ALM) is used to model the wind turbine blades by means of body forces added to the momentum equation. The fluid dynamics video shows the root and tip vortices emanating from the blades from various viewpoints. The vortices become unstable and break down into large-scale turbulent structures. As the wakes of the wind turbines advect further downstream, smaller-scale turbulence is generated. It is apparent that vortices generated by the blades of the downstream wind turbine break down faster due to increased turbulence levels generated by the wake of the upstream wind turbine.
The estimation of extreme loads from waves is an essential part of the design of an offshore wind turbine. Standard design codes suggest to either use simplified methods based on regular waves, or to perform fully nonlinear computations. The former might not provide an accurate representation of the extreme waves, while the latter is computationally too intensive for design iterations. We address these limitations by using the fully nonlinear solver OceanWave3D to establish the DeRisk database, a large dataset of extreme waves kinematics in a two-dimensional domain. From the database, which is open and freely available, a designer can extract fully-nonlinear wave kinematics for a wave condition and water depth of interest by identifying a suitable computation in the database and, if needed, by Froude-scaling the kinematics. The nonlinear solver is validated against the DeRisk model experiments at two different water depths, $33.0 [m]$ and $20.0 [m]$, and an excellent agreement is found for the analyzed cases. The experiments are used to calibrate OceanWave3Ds numerical breaking filter constant, and the best agreement is found for $beta=0.5$. We compare the experimental static force with predictions by the DeRisk database and the Rainey force model, and with state-of-the-art industrial practices. For milder storms, we find a good agreement in the predicted extreme force between the present methodology and the standard methodologies. At the deep location and for stronger storms, the largest loads are given by slamming loads due to breaking waves. In this condition, the database methodology is less accurate than the embedded stream function method and more accurate than the WiFi JIP methodology, providing generally nonconservative estimates. For strong storms at the shallower location, where wave breaking is less dominating, the database methodology is the most accurate overall.
Super-large-scale particle image velocimetry and flow visualization with natural snowfall is used to collect and analyze multiple datasets in the near wake of a 2.5 MW wind turbine. Each dataset captures the full vertical span of the wake from a different perspective. Together, these datasets compose a three-dimensional picture of the near-wake flow, including the effect of the tower and hub and the variation of instantaneous wake expansion in response to changes in turbine operation. A region of high-speed flow is observed directly behind the hub, and a region of low-speed flow appears behind the tower. Additionally, the hub produces a region of enhanced turbulence in its wake while the tower reduces turbulence near the ground as it breaks up turbulent structures in the boundary layer. Analysis of the instantaneous wake behaviour reveals variations in wake expansion, and even periods of wake contraction, occurring in response to changes in the angle of attack and blade pitch gradient. This behaviour is found to depend on the region of operation of the turbine. These findings can be incorporated into wake models and advanced control algorithms for wind farm optimization and can be used to validate wind turbine wake simulations.
The current study uses large eddy simulations to investigate the transient response of a utility-scale wind turbine wake to dynamic changes in atmospheric and operational conditions, as observed in previous field-scale measurements. Most wind turbine wake investigations assume quasi-steady conditions, but real wind turbines operate in a highly stochastic atmosphere, and their operation (e.g., blade pitch, yaw angle) changes constantly in response. Furthermore, dynamic control strategies have been recently proposed to optimize wind farm power generation and longevity. Therefore, improved understanding of dynamic wake behaviors is essential. First, changes in blade pitch are investigated and the wake expansion response is found to display hysteresis as a result of flow inertia. The timescales of the wake response to different pitch rates are quantified. Next, changes in wind direction with different timescales are explored. Under short timescales, the wake deflection is in the opposite direction of that observed under quasi-steady conditions. Finally, yaw changes are implemented at different rates, and the maximum inverse wake deflection and timescale are quantified, showing a clear dependence on yaw rate. To gain further physical understanding of the mechanism behind the inverse wake deflection, the streamwise vorticity in different parts of the wake is quantified. The results of this study provide guidance for the design of advanced wake flow control algorithms. The lag in wake response observed for both blade pitch and yaw changes shows that proposed dynamic control strategies must implement turbine operational changes with a timescale on the order of the rotor timescale or slower.
Super-large-scale particle image velocimetry (SLPIV) using natural snowfall is used to investigate the influence of nacelle and tower generated flow structures on the near-wake of a 2.5 MW wind turbine at the EOLOS field station. The analysis is based on the data collected in a field campaign on March 12th, 2017, with a sample area of 125 m (vertical) x 70 m (streamwise) centred on the plane behind the turbine support tower. The SLPIV measurement provides the velocity field over the entire rotor span, revealing a region of accelerated flow around the hub caused by the reduction in axial induction at the blade roots. The in-plane turbulent kinetic energy field shows an increase in turbulence in the regions of large shear behind the blade tips and the hub, and a reduction in turbulence behind the tower where the large-scale turbulent structures in the boundary layer are broken up. Snow voids reveal coherent structures shed from the blades, nacelle, and tower. The hub wake meandering frequency is quantified and found to correspond to the vortex shedding frequency of an Ahmed body (St=0.06). Persistent hub wake deflection is observed and shown to be connected with the turbine yaw error. In the region below the hub, strong interaction between the tower- and blade-generated structures is observed. The temporal characteristics of this interaction are quantified by the co-presence of two dominant frequencies, one corresponding to the blade vortex shedding at the blade pass frequency and the other corresponding to tower vortex shedding at St=0.2. This study highlights the influence of the tower and nacelle on the behaviour of the near-wake, informing model development and elucidating the mechanisms that influence wake evolution.
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