Mads Baungaard’s research while affiliated with Technical University of Denmark and other places

Wind turbines in an offshore wind farm typically have the same hub height, and in this case, the power of a wind farm could be predicted if the flow field in the horizontal 2D plane at the hub height is predicted accurately. Nevertheless, Reynolds-averaged Navier-Stokes (RANS) simulations of wind farm flows are predominantly made in full 3D domains, which are naturally more computationally expensive than 2D simulations. In this work, a systematic comparison is made between 2D and 3D RANS simulations of various wind farm configurations to assess the differences in computational cost and accuracy. For our numerical setup and the cases considered, which include layouts with up to 144 turbines, it is found that the 2D simulations are at least two orders of magnitude computationally cheaper than their corresponding 3D simulations, while the predicted farm power is within -30 % to 15 % for all cases. Only minor, but necessary, modifications have been made to the governing 2D RANS equations to avoid unphysical decay of turbulence, allowing for a simple direct comparison between the 2D to 3D simulations. Given the low computational cost and already sensible performance of the only slightly modified 2D RANS simulations demonstrated in this work, it appears attractive to further investigate this methodology and possibly introduce additional 2D modifications to improve the accuracy in future work.

Wind turbines are increasing in size and operate more frequently above the atmospheric surface layer, which requires improved inflow models for numerical simulations of turbine interaction. In this work, a steady-state Reynolds-averaged Navier–Stokes (RANS) model of the neutral and stable atmospheric boundary layer (ABL) is introduced. The model incorporates buoyancy in the turbulence closure equations using a prescribed Brunt–Väisälä frequency, does not require a global turbulence length-scale limiter, and is only dependent on two non-dimensional numbers. Assuming a constant temperature gradient over the entire ABL, although a strong assumption, leads to a simple and well-behaved inflow model. RANS wake simulations are performed for shallow and tall ABLs, and the results show good agreement with large-eddy simulations in terms of velocity deficit from a single wind turbine. However, the proposed RANS model underpredicts the magnitude of the velocity deficit of a wind turbine row for the shallow ABL case. In addition, RANS ABL models can suffer from numerical problems when they are applied as a shallow-ABL inflow model to large wind farms due to the low-eddy-viscosity layer above the ABL. The proposed RANS model inherits this issue, and further research is required to solve it.

Energy losses due to wind farm clustering and wind farm interaction are rarely well represented in the wind farm design process because of the lack of fast models that can accurately account for neighboring wind farm wakes. A recently developed solution is the actuator wind farm (AWF) model, which is a Reynolds-averaged Navier-stokes (RANS) based wind farm parametrization that models a wind farm as a distributed thrust force and applies a global wind farm thrust coefficient controller. We propose an improved version of the AWF model, where each turbine employs a local thrust force controller and uses turbine thrust and power coefficients as input to better handle inhomogeneous inflow conditions. The proposed AWF model shows improved performance compared to the original AWF model in terms of predicted wind turbine power of a downstream wind farm that operates in a partial wake of an upstream wind farm, without significantly increasing the computational effort. However, the annual energy production (AEP) wake losses of a large wind farm cluster are nearly unaffected by using local or global control and input because the largest impact is found near the cut-in wind speed, which does not contribute much to the AEP wake losses.

Wind turbines are increasing in size and operate more frequently above the atmospheric surface layer, which requires improved inflow models for numerical simulations of turbine interaction. In this work, a steady-state Reynolds-averaged Navier-Stokes (RANS) model of the neutral and stable atmospheric boundary layer (ABL) is introduced. The model employs a buoyancy source using a prescribed Brunt-Väisälä frequency, does not require a global turbulence length scale limiter, and is only dependent on two non-dimensional numbers. The proposed model assumes a constant temperature gradient over the entire ABL, which is a strong assumption but leads to a simple and well behaving inflow model. RANS wake simulations subjected to shallow and tall ABLs are performed and the results show a good agreement with results from two different large-eddy simulation codes in terms of velocity deficit.

Reynolds-averaged Navier-Stokes (RANS) simulations of a single wind turbine wake in the neutral atmospheric pressure-driven boundary layer (PDBL) are conducted and compared to RANS simulations with inflow based on the more traditional log-law. The latter is valid in the neutral atmospheric surface layer (ASL), while the PDBL is a better representation of the whole atmospheric boundary layer (ABL). It is found that the wake results of the two types of simulations become more similar for increasing ABL height to rotor diameter ratio. In fact, the ASL is shown to be a special asymptotic case of the PDBL. The RANS simulations are also compared to a large-eddy simulation (LES) PDBL case, where it is found that both the ASL and PDBL RANS simulations compare well with the reference LES data in the wake region, while the RANS PDBL compares better with the data in the upper region of the domain.

Understanding wind turbine wake recovery is important for developing models of wind turbine interaction employed in the design of energy-efficient wind farm layouts. Wake recovery is often assumed or explained to be a shear-driven process; however, this is generally not accurate. In this work we show that wind turbine wakes recover mainly due to the divergence (lateral and vertical gradients) of Reynolds shear stresses, which transport momentum from the freestream towards the wake center. The wake recovery mechanisms are illustrated using a simple analytic model and results of large-eddy simulation.

Reynolds-averaged Navier–Stokes (RANS) simulations of wind turbine wakes are usually conducted with two-equation turbulence models based on the Boussinesq hypothesis; these are simple and robust but lack the capability of predicting various turbulence phenomena. Using the explicit algebraic Reynolds stress model (EARSM) of can alleviate some of these deficiencies while still being numerically robust and only slightly more computationally expensive than the traditional two-equation models. The model implementation is verified with the homogeneous shear flow, half-channel flow, and square duct flow cases, and subsequently full three-dimensional wake simulations are run and analyzed. The results are compared with reference large-eddy simulation (LES) data, which show that the EARSM especially improves the prediction of turbulence anisotropy and turbulence intensity but that it also predicts less Gaussian wake profile shapes.

Wind farm flow control (WFFC) is a topic of interest at several research institutes and industry and certification agencies worldwide. For reliable performance assessment of the technology, the efficiency and the capability of the models applied to WFFC should be carefully evaluated. To address that, the FarmConners consortium has launched a common benchmark for code comparison under controlled operation to demonstrate its potential benefits, such as increased power production. The benchmark builds on available data sets from previous field campaigns, wind tunnel experiments, and high-fidelity simulations. Within that database, four blind tests are defined and 13 participants in total have submitted results for the analysis of single and multiple wakes under WFFC. Here, we present Part I of the FarmConners benchmark results, focusing on the blind tests with large-scale rotors. The observations and/or the model outcomes are evaluated via direct power comparisons at the upstream and downstream turbine(s), as well as the power gain at the wind farm level under wake steering control strategy. Additionally, wake loss reduction is also analysed to support the power performance comparison, where relevant. The majority of the participating models show good agreement with the observations or the reference high-fidelity simulations, especially for lower degrees of upstream misalignment and narrow wake sector. However, the benchmark clearly highlights the importance of the calibration procedure for control-oriented models. The potential effects of limited controlled operation data in calibration are particularly visible via frequent model mismatch for highly deflected wakes, as well as the power loss at the controlled turbine(s). In addition to the flow modelling, the sensitivity of the predicted WFFC benefits to the turbine representation and the implementation of the controller is also underlined. The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of farm flow control benefits. It forms an important basis for more detailed benchmarks in the future with extended control objectives to assess the true value of WFFC.

Understanding wind turbine wake recovery is important for developing models of wind turbine interaction employed in the design of energy-efficient wind farm layouts. Wake recovery is often assumed or explained to be a shear-driven process; however, this is generally not accurate. In this work we show that wind turbine wakes recover mainly due to the divergence (lateral and vertical gradients) of Reynolds shear stresses, which transport momentum from the freestream towards the wake center. The wake recovery mechanisms are illustrated using a simple analytic model and results of large-eddy simulation.

Reynolds-averaged Navier-Stokes (RANS) simulations of wind turbine wakes are usually conducted with two-equation turbulence models based on the Boussinesq hypothesis, which are simple and robust but lack the capability of predicting various turbulence phenomena. Using the explicit algebraic Reynolds stress model (EARSM) of Wallin and Johansson (2000) can aid some of these deficiencies, while still being numerical robust and only slightly more computationally expensive than the traditional two-equation models. The model implementation is verified with the homogeneous shear flow, half-channel flow and square duct flow cases, and subsequently full 3D wake simulations are run and analyzed. The results are compared with reference large eddy simulation (LES) data, which shows that the EARSM especially improves the prediction of turbulence anisotropy and turbulence intensity but that it also predicts less Gaussian shaped wake profiles with the standard settings of the model.