In this numerical study, we use a multi-scale version of physics-informed neural network (PINN) for wind field reconstruction from LiDAR measurements. The reference velocity field is obtained from high-fidelity large-eddy simulation of neutral atmospheric boundary layer, and the LiDAR measurement strategy is restricted to that of a real LiDAR. The multi-scale PINN reconstructs the velocity field by minimizing a combination of the L2-error with respect to the LiDAR measurements and residuals of the governing equations. Our most significant finding is that adding a multi-scale layer to PINN enables us to: (i) capture wider range of scales, (ii) reconstruct the flow field outside the LiDAR scanning area, and (iii) reach faster convergence. We also find that for volumetric flow reconstruction and to deal with uncertainty in the wind direction, the reconstruction accuracy can be greatly improved by employing multiple LiDAR devices. Overall, our results show that the normalized errors in the reconstructed wind field are lower than 5% for all the experiments conducted in this study and that the errors do not increase even in the presence of measurement noise levels of typical LiDAR. These findings show the feasibility of three-dimensional dynamic wind field reconstruction across large wind farms using LiDAR devices.

We present an improved dynamic model to predict the time-varying characteristics of the far-wake flow behind a wind turbine. Our model, based on the FAST.Farm engineering model, is novel in that it estimates the turbulence generated by convective instabilities, which selectively amplifies the inflow velocity fluctuations. Our model also incorporates scale dependence when calculating the wake meandering induced by the passive wake meandering mechanism. For validation, our model is compared with FAST.Farm and large-eddy simulation (LES). For the mean flow, our model agrees well with LES in terms of the wake deficit and wake width, but the FAST.Farm model underestimates the former and overestimates the latter. For the instantaneous flow, our model predicts well the wake-center deflection and turbulent kinetic energy, reducing the discrepancies in the spectral characteristics by more than a factor of two relative to LES, depending on the Strouhal number. By incorporating two key mechanisms governing the far-wake dynamics, our model can predict more accurately the dynamic wake evolution, making it suitable for real-time calculations of wind farm performance.

A thorough understanding of the energetic flow structures that form in the far wake of a wind turbine is essential for accurate turbine wake modeling and wind farm performance estimation. We use resolvent analysis to predict such flow structures for a turbine operating in a neutral atmospheric boundary layer and validate our results against data-driven modes extracted through spectral proper orthogonal decomposition. The forcing and response modes calculated from resolvent analysis reveal the upstream forcing locations that are most influential in generating turbulent kinetic energy (TKE) in the far wake. Additionally, resolvent analysis shows the important role of transverse forcing and contribution of the non-modal Orr mechanism in TKE generation. The resolvent analysis method requires only the mean wake velocity and eddy viscosity profiles as inputs but can capture the energetic modes and TKE spectra in the far wake. In this specific application, the resolvent analysis method approximates the wake to be axisymmetric, which suggests that it can be paired with engineering wake models. Overall this study demonstrates the use of resolvent analysis as a viable tool for estimating TKE and for uncovering the mechanism of TKE generation.

The development of digital twins for wind farms often involves the use of large-eddy simulation (LES) to model atmospheric boundary layers. Existing LES solvers primarily focus on accurately capturing streamwise fluctuations. They, however, overlook the less energetic cross-stream fluctuations, which play a crucial role in wind turbine wake evolution. In this study, we conduct a systematic parametric study and incorporate changes in an open-source LES solver. The improved solver is able to predict all three components of velocity fluctuations in alignment with the scaling laws derived from the attached-eddy hypothesis. In particular, we examine the impact of (i) the subgrid-scale model, (ii) the wall model, (iii) the von Kármán constant, and (iv) the grid-cell aspect ratio. We find that although all these factors influence the prediction of velocity fluctuations, the grid-cell aspect ratio has the greatest effect on the spanwise and vertical velocity components. Notably, utilizing nearly isotropic grid cells leads to the best alignment of all three velocity component fluctuations with the scaling laws. Spectral analysis further demonstrates that the present LES solver accurately predicts the characteristic length scales for all velocity fluctuation components, making it a reliable tool for obtaining turbulent inflow conditions for wind farm modeling.

Wind energy is crucial to the transition to a carbon-free world. However, new wind farms are increasingly sited on complex terrain, whose influence on turbine performance is still not well understood. Here large-eddy simulations are performed on the flow around a wind turbine sited on three different terrain types: a flat ground, a 2-D hill, and a 3-D hill. We find that hilly terrain can increase the power generated via the speed-up effect, but that it can also increase the wake deficit and deflect the wake center, potentially affecting any turbines downstream. We interpret this deflection as being caused by the topography-induced vertical velocity component, which we model with a passive tracer method. By combining this passive tracer method with engineering-focused wake models, we obtain improved predictions of the velocity deficit and wake deflection. Such a hybrid strategy is fast and accurate, facilitating the design of wind farms sited on steep hilly terrain, which often experience flow separation at the backslope.

Wake meandering and turbulent kinetic energy (TKE) generation in the far-wake region of wind turbines significantly affect the power production and aerodynamic loads of wind farms. This work thus aims at understanding the componentwise influence of upstream turbulence and roles of different mechanisms on the far-wake dynamics to guide the development of wind-farm wake models. We find that the wake meandering is mainly caused by the upstream spanwise (v ^′) and vertical (w ^′) velocity fluctuations, supporting the passive wake meandering mechanism. However, our results also show a scale-dependence of the wake meandering that should be accounted in wake models. We find that v ^′ and w ^′ cause greater TKE generation than the streamwise velocity fluctuations (u ^′). We then use simulation- and resolvent-based componentwise input–output analyses to explain that this is because the shear instability in turbine wakes is more receptive to the transverse forcing relative to the streamwise forcing. This highlights the importance of implementing the shear instability mechanism in wake models for accurate TKE estimations. Finally, we find that u ^′ cause the thrust fluctuations, which can lead to near-wake corrections and hence influence the far-wake evolution.