Accurately predicting wind turbine wake effects is essential for optimizing wind-farm performance and minimizing maintenance costs. This study explores the applicability of the Sparse Regression of Turbulent Stress Anisotropy (SpaRTA) framework to develop a simple yet robust Reynolds-averaged Navier-Stokes (RANS) model for wake prediction in wind energy contexts. The framework introduces two correction terms into two-equation models, with k - ϵ model being utilized in the current study. One correction term resembles the residual of the Turbulent Kinetic Energy (TKE) equation, and the other corrects the deviatoric part of the Reynolds Stress Tensor (RST). The terms are calculated from high-fidelity measurement or simulation data, and symbolic regression is used to determine the model for these terms. In this study, Large Eddy Simulation (LES) data from a single turbine is used as the training dataset, and a sample pre-selection process is employed to discover a correction model efficiently. The derived model incorporates two terms based on Pope's basis tensors and their invariants. The expression of the obtained model shows that it functions as a modification to the constant Cμ in the k - ϵ model. The model is evaluated by comparing its predicted velocity and TKE fields with the LES data used for the training. The model showed satisfactory performance in predicting both fields. Additionally, its generalizability is evaluated by testing it against a more complex six-turbine unseen case. The results indicate that the model effectively captures the velocity field and power output, but it tends to overpredict TKE, especially in the wake region.

The state-of-the-art in wind-farm flow-physics modeling is Large Eddy Simulation (LES) which makes accurate predictions of most relevant physics, but requires extensive computational resources. The next-fidelity model types are Reynolds-Averaged Navier–Stokes (RANS) which are two orders of magnitude cheaper, but resolve only mean quantities and model the effect of turbulence. They often fail to accurately predict key effects, such as the wake recovery rate. Custom RANS closures designed for wind-farm wakes exist, but so far do not generalize well: there is substantial room for improvement. In this article we present the first steps towards a systematic data-driven approach to deriving new RANS models in the wind-energy setting. Time-averaged LES data is used as ground-truth, and we first derive optimal corrective fields for the turbulence anisotropy tensor and turbulence kinetic energy (t.k.e.) production. These fields, when injected into the RANS equations (with a baseline k–ɛ model) reproduce the LES mean-quantities. Next we build a custom RANS closure from these corrective fields, using a deterministic symbolic regression method to infer algebraic correction as a function of the (resolved) mean-flow. The result is a new RANS closure, customized to the training data. The potential of the approach is demonstrated under neutral atmospheric conditions for multi-turbine constellations at wind-tunnel scale. The results show significantly improved predictions compared to the baseline closure, for both mean velocity and the t.k.e. fields.

Data-driven Reynolds-averaged Navier–Stokes (RANS) turbulence closures are increasing seen as a viable alternative to general-purpose RANS closures, when LES reference data is available—also in wind-energy. Parsimonious closures with few, simple terms have advantages in terms of stability, interpret-ability, and execution speed. However experience suggests that closure model corrections need be made only in limited regions—e.g. in the near-wake of wind turbines and not in the majority of the flow. A parsimonious model therefore must find a middle ground between precise corrections in the wake, and zero corrections elsewhere. We attempt to resolve this impasse by introducing a classifier to identify regions needing correction, and only fit and apply our model correction there. We observe that such classifier-based models are significantly simpler (with fewer terms) than models without a classifier, and have similar accuracy, but are more prone to instability. We apply our framework to three flows consisting of multiple wind-turbines in neutral conditions with interacting wakes.

Currently, the state of the art in wind farm flow physics modeling are Large Eddy Simulations (LES) which resolve a large part of the spectra of the turbulent fluctuations. But this type of model requires extensive computational resources. One wind speed and direction simulation of the Lillgrund wind farm can take between 160k and 3000k processor hours depending on how the turbines are modeled [1, 2]. The next-fidelity model types are Reynolds-Averaged Navier-Stokes (RANS) models which resolve only the mean quantities and model the effect of turbulence fluctuations. These models require about two orders of magnitude less computational time, but generally do not produce accurate predictions of the mean flow field. Proposed modifications made to these models so far do not generalize well and there is room for improvement. Hence, we present the first steps towards using a data-driven approach to aid in deriving new RANS models that generalize well to different turbine types, varying atmospheric stability, and farm layouts. To do so, time-averaged LES data is used to derive corrections to existing RANS models. The approach uses a deterministic symbolic regression method to infer algebraic correction terms to the RANS turbulence transport equations. Optimal correction terms to the RANS equations are derived using a frozen approach where time-averaged flow fields from LES are injected into the RANS equations. The potential of the approach is demonstrated under neutral conditions for multi-turbine constellations at wind-tunnel scale. The results show promise, but more work is necessary to realize the full potential of the approach.

Standard passive aerodynamic flow control devices such as vortex generators and gurney flaps have a working principle that is well understood. They increase the stall angle and the lift below stall and are mainly applied at the inboard part of wind turbine blades. However, the potential of applying a rigidly fixed leading-edge slat element at inboard blade stations is less well understood but has received some attention in the past decade. This solution may offer advantages not only under steady conditions but also under unsteady inflow conditions such as yaw. This article aims at further clarifying what an optimal two-element configuration with a thick main element would look like and what kind of performance characteristics can be expected from a purely aerodynamic point of view. To accomplish this an aerodynamic shape optimization procedure is used to derive optimal profile designs for different optimization boundary conditions including the optimization of both the slat and the main element. The performance of the optimized designs shows several positive characteristics compared to single-element airfoils, such as a high stall angle, high lift below stall, low roughness sensitivity, and higher aerodynamic efficiency. Furthermore, the results highlight the benefits of an integral design procedure, where both slat and main element are optimized, over an auxiliary one. Nevertheless, the designs also have two caveats, namely a steep drop in lift post-stall and high positive pitching moments.