Modeling turbine wakes and power losses within a wind farm using LES: An application to the Horns Rev offshore wind farm

A modeling framework is proposed and validated to simulate turbine wakes and associated power losses in wind farms. It combines the large-eddy simulation (LES) technique with blade element theory and a turbine-model-specific relationship between shaft torque and rotational speed. In the LES, the turbulent subgrid-scale stresses are parameterized with a tuning-free Lagrangian scale-dependent dynamic model. The turbine-induced forces and turbine-generated power are modeled using a recently developed actuator-disk model with rotation (ADM-R), which adopts blade element theory to calculate the lift and drag forces (that produce thrust, rotor shaft torque and power) based on the local simulated flow and the blade characteristics. In order to predict simultaneously the turbine angular velocity and the turbine-induced forces (and thus the power output), a new iterative dynamic procedure is developed to couple the ADM-R turbine model with a relationship between shaft torque and rotational speed. This relationship, which is unique for a given turbine model and independent of the inflow condition, is derived from simulations of a stand-alone wind turbine in conditions for which the thrust coefficient can be validated. Comparison with observed power data from the Horns Rev wind farm shows that better power predictions are obtained with the dynamic ADM-R than with the standard ADM, which assumes a uniform thrust distribution and ignores the torque effect on the turbine wakes and rotor power. The results are also compared with the power predictions obtained using two commercial wind-farm design tools (WindSim and WAsP). These models are found to underestimate the power output compared with the results from the proposed LES framework.

Large-Eddy Simulation of Turbulent Boundary Layer Flow through Wind Turbines and Wind Farms

Yu-Ting Wu

In this thesis, we develop a new large-eddy simulation (LES) framework to simulate atmospheric boundary layer (ABL) flows through wind turbines and wind farms. A Lagrangian scale-dependent dynamic model is used to compute the Smagorinsky model coefficient dynamically based on the local dynamics of the resolved velocity field. The turbine-generated power outputs and the turbine-induced forces (e.g., thrust, lift, drag) are parameterized using two actuator-disk models: (a) the traditional actuator-disk model without rotation (ADM-NR), which uses 1D momentum theory to relate the power output and the uniform thrust force distribution with an incoming velocity; and (b) the actuator-disk model with rotation (ADM-R), which adopts blade element theory to calculate the lift and drag forces (that produce thrust, rotor shaft torque, and power) based on the local blade and flow characteristics. The performance of the LES framework is first evaluated through comparisons with high-resolution velocity measurements collected in the wind-tunnel experiments with the single wake of a stand-alone miniature wind turbine [Chamorro and Porté-Agel, 2010a] as well as the multiple turbine wakes in a model aligned wind farm [Chamorro and Porté-Agel, 2011]. Emphasis is placed on the structure and characteristics of the simulated turbine wakes using the ADM-NR and the ADM-R. In general, the ADM-R yields improved predictions compared with the ADM-NR in the wake regions, where the ADM-NR tends to underestimate the velocity deficit and the enhancement of turbulence intensity in the wakes. Next, the LES framework is used to model multiple turbine wakes and associated power losses in a large wind farm. Here, we propose a new dynamic procedure coupled with the ADM-R to predict turbine power output based on a turbine-model-specific relationship between the shaft torque and the blade angular speed. The Horns Rev offshore wind farm is chosen as a case study since both power data from eighty Vestas V80 wind turbines and flow data from three nearby meteorological masts were available [Barthelmie et al., 2009]. The torque-speed relationship for the V80 turbine is obtained from a series of stand-alone turbine simulations. In the wind farm simulations, the ADM-R gives the best power prediction. Finally, the validated LES framework is used to study atmospheric turbulence effects on wind-turbine wakes in neutrally-stratified ABL over homogeneous flat surfaces with four different aerodynamic roughness lengths. In this study, the simulation result shows that the different turbulence intensity levels of the incoming flow lead to considerable influence on the spatial distribution of the mean velocity deficit, turbulence intensity, and turbulent shear stress in the wake region. In particular, when the turbulence intensity level of the incoming flow is higher, the turbine-induced wake (velocity deficit) recovers faster, and the locations of the maximum turbulence intensity and turbulent stress are closer to the turbine.

EPFL2013

Simulation of Turbulent Flow Inside and Above Wind Farms: Model Validation and Layout Effects

Fernando Porté Agel, Yu-Ting Wu

A recently-developed large-eddy simulation framework is validated and used to investigate turbulent flow within and above wind farms under neutral conditions. Two different layouts are considered, consisting of thirty wind turbines occupying the same total area and arranged in aligned and staggered configurations, respectively. The subgrid-scale (SGS) turbulent stress is parametrized using a tuning-free Lagrangian scale-dependent dynamic SGS model. The turbine-induced forces are modelled using two types of actuator-disk models: (a) the 'standard' actuator-disk model (ADM-NR), which calculates only the thrust force based on one-dimensional momentum theory and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses blade-element momentum theory to calculate the lift and drag forces (that produce both thrust and rotation), and distributes them over the rotor disk based on the local blade and flow characteristics. Validation is performed by comparing simulation results with turbulence measurements collected with hot-wire anemometry inside and above an aligned model wind farm placed in a boundary-layer wind tunnel. In general, the ADM-R model yields improved predictions compared with the ADM-NR in the wakes of all the wind turbines, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces in the ADM-R appear to be important. Another advantage of the ADM-R model is that, unlike the ADM-NR, it does not require a priori specification of the thrust coefficient (which varies within a wind farm). Finally, comparison of simulations of flow through both aligned and staggered wind farms shows important effects of farm layout on the flow structure and wind-turbine performance. For the limited-size wind farms considered in this study, the lateral interaction between cumulated wakes is stronger in the staggered case, which results in a farm wake that is more homogeneous in the spanwise direction, thus resembling more an internal boundary layer. Inside the staggered farm, the relatively longer separation between consecutive downwind turbines allows the wakes to recover more, exposing the turbines to higher local wind speeds (leading to higher turbine efficiency) and lower turbulence intensity levels (leading to lower fatigue loads), compared with the aligned farm. Above the wind farms, the area-averaged velocity profile is found to be logarithmic, with an effective wind-farm aerodynamic roughness that is larger for the staggered case.

Springer Netherlands2013

Large-Eddy Simulation of Wind-Turbine Wakes: Evaluation of Turbine Parametrisations

Fernando Porté Agel, Yu-Ting Wu

Large-eddy simulation (LES), coupled with a wind-turbine model, is used to investigate the characteristics of a wind-turbine wake in a neutral turbulent boundary-layer flow. The tuning-free Lagrangian scale-dependent dynamic subgrid-scale (SGS) model is used for the parametrisation of the SGS stresses. The turbine-induced forces (e.g., thrust, lift and drag) are parametrised using two models: (a) the 'standard' actuator-disk model (ADM-NR), which calculates only the thrust force and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses the blade-element theory to calculate the lift and drag forces (that produce both thrust and rotation), and distribute them over the rotor disk based on the local blade and flow characteristics. Simulation results are compared to high-resolution measurements collected with hot-wire anemometry in the wake of a miniature wind turbine at the St. Anthony Falls Laboratory atmospheric boundary-layer wind tunnel. In general, the characteristics of the wakes simulated with the proposed LES framework are in good agreement with the measurements in the far-wake region. The ADM-R yields improved predictions compared with the ADM-NR in the near-wake region, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces appear to be important. Our results also show that the Lagrangian scale-dependent dynamic SGS model is able to account, without any tuning, for the effects of local shear and flow anisotropy on the distribution of the SGS model coefficient.

Springer Netherlands2011

Simulation of Turbulent Flow Inside and Above Wind Farms: Model Validation and Layout Effects

Fernando Porté Agel, Yu-Ting Wu

Springer Netherlands2013

Large-Eddy Simulation of Turbulent Boundary Layer Flow through Wind Turbines and Wind Farms

Yu-Ting Wu

EPFL2013