Analytical solution for the cumulative wake of wind turbines in wind farms

This paper solves an approximate form of conservation of mass and momentum for a turbine in a wind farm array. The solution is a fairly simple explicit relationship that predicts the streamwise velocity distribution within a wind farm with an arbitrary layout. As this model is obtained by solving flow-governing equations directly for a turbine that is subject to upwind turbine wakes, no ad hoc superposition technique is needed to predict wind farm flows. A suite of large-eddy simulations (LES) of wind farm arrays is used to examine self-similarity as well as validity of the so-called conservation of momentum deficit for turbine wakes in wind farms. The simulations are performed with and without the presence of some specific turbines in the wind farm. This allows us to systematically study some of the assumptions made to develop the analytical model. A modified version of the conservation of momentum deficit is also proposed to provide slightly better results at short downwind distances, as well as in the far wake of turbines deep inside a wind farm. Model predictions are validated against the LES data for turbines in both full-wake and partial-wake conditions. While our results highlight the limitation in capturing the flow speed-up between adjacent turbine columns, the model is overall able to acceptably predict flow distributions for a moderately sized wind farm. Finally, the paper employs the new model to provide insights on the accuracy of common wake superposition methods

Wind Turbine Modeling for Computational Fluid Dynamics: December 2010 - December 2012

With the shortage of fossil fuel and the increasing environmental awareness, wind energy is becoming more and more important. As the market for wind energy grows, wind turbines and wind farms are becoming larger. Current utility-scale turbines extend a significant distance into the atmospheric boundary layer. Therefore, the interaction between the atmospheric boundary layer and the turbines and their wakes needs to be better understood. The turbulent wakes of upstream turbines affect the flow field of the turbines behind them, decreasing power production and increasing mechanical loading. With a better understanding of this type of flow, wind farm developers could plan better-performing, less maintenance-intensive wind farms. Simulating this flow using computational fluid dynamics is one important way to gain a better understanding of wind farm flows. In this study, we compare the performance of actuator disc and actuator line models in producing wind turbine wakes and the wake-turbine interaction between multiple turbines. We also examine parameters that affect the performance of these models, such as grid resolution, the use of a tip-loss correction, and the way in which the turbine force is projected onto the flow field

Floating Platform Effects on Power Generation in Spar and Semisubmersible Wind Turbines

The design and financing of commercial-scale floating offshore wind projects require a better understanding of how power generation differs between newer floating turbines and well-established fixed-bottom turbines. In floating turbines, platform mobility causes additional rotor motion that can change the time-averaged power generation. In this work, OpenFAST simulations examine the power generated by the National Renewable Energy Laboratory\u27s 5-MW reference turbine mounted on the OC3-UMaine spar and OC4-DeepCWind semisubmersible floating platforms, subjected to extreme irregular waves and below-rated turbulent inflow wind from large-eddy simulations of a neutral atmospheric boundary layer. For these below-rated conditions, average power generation in floating turbines is most affected by two types of turbine displacements: an average rotor pitch angle that reduces power, caused by platform pitch; and rotor motion upwind-downwind that increases power, caused by platform surge and pitch. The relative balance between these two effects determines whether a floating platform causes power gains or losses compared to a fixed-bottom turbine; for example, the spar creates modest (3.1%-4.5%) power gains, whereas the semisubmersible creates insignificant (0.1%-0.2%) power gains for the simulated conditions. Furthermore, platform surge and pitch motions must be analyzed concurrently to fully capture power generation in floating turbines, which is not yet universal practice. Finally, a simple analytical model for predicting average power in floating turbines under below-rated wind speeds is proposed, incorporating effects from both the time-averaged pitch displacement and the dynamic upwind-downwind displacements