arXiv subjects

Majid Bastankhah

Publications and source records attributed to Majid Bastankhah.

11 recordsLinked to original sources

arXiv2026

Two-way coupling of gravity waves and wind farm wakes: a reduced-order boundary-layer model

This paper develops a reduced-order numerical framework for modelling the two-way coupling between gravity waves and turbulent wakes in large-scale wind farms. Starting with the non-hydrostatic Boussinesq equations and introducing simplifications appropriate to the boundary layer and the overlying stratified free atmosphere yield separate governing equations for the two regions. These are coupled through a dynamic boundary condition at the capping inversion, which directly captures the feedback of gravity waves on the boundary-layer flow. A mixed pseudo-spectral finite-difference discretisation yields a computationally efficient model while retaining vertical boundary-layer structure. For the semi-infinite wind farm considered here, a complete solution is obtained in a matter of seconds on a standard laptop. Comparisons with large-eddy simulations (LES) confirm the model successfully reproduces both internal wind-farm flow and large-scale gravity-wave effects. It captures the upstream blockage induced by adverse pressure gradients, as well as the accelerated wake recovery within and downwind of the farm, driven by favourable pressure gradients.

physics.flu-dyn↗

arXiv2026

Generalised actuator disk theory: wake development with turbulent entrainment

Classical actuator disk theory, developed more than a century ago, provides an idealised description of turbine rotor performance. It treats a rotor as an infinitesimally-thin permeable disk and applies the governing flow equations over a streamtube encompassing the disk. A well-known limitation of the theory is its assumption of ideal flow downstream of the disk, which restricts its applicability to short downwind distances before turbulence and mixing processes governing the wake evolution take hold. The classical theory also leads to unphysical predictions of thrust and power coefficients for highly-loaded rotors. Turbulent axisymmetric wakes, by contrast, represent an extensively-studied canonical free shear flow with much of the progress and its applications to wind turbines limited to the far-wake dynamics. In this work, we introduce a generalised actuator disk theory based on a hybrid stream-tube and wake control volume, that seamlessly integrates classical actuator disk analysis with wake turbulence modelling at arbitrary distances from the rotor. The resulting model, while still idealised, can be used to predict variations in velocity, pressure, and cross-sectional flow area as function of position, both upstream and downstream of the rotor disk. Furthermore, by accounting for turbulent entrainment in the wake development, it provides more realistic predictions of thrust and power coefficients for highly-loaded disks.

physics.flu-dyn↗

arXiv2026

Assessing engineering wake models against operational data: insights from the Lillgrund wind farm wake steering campaign

Validating engineering wake models under real-world operational conditions is essential for improving wind farm performance predictions. This study uses a unique dataset from the Lillgrund offshore wind farm, collected during the Horizon 2020 TotalControl campaign, integrating synchronous Supervisory Control and Data Acquisition (SCADA) and Light Detection and Ranging (LiDAR) measurements under both baseline operation and active wake steering conditions. Four analytical wake-model combinations, implemented in the LongSim software developed by DNV, are evaluated using different formulations for velocity deficit, added turbulence, wake superposition and wake deflection. The analysis focuses on time-averaged wake velocity deficit profiles and turbine- and farm-wide power output, normalised by reference velocity and power. Model accuracy is assessed using mean absolute error (MAE) metrics. The models generally reproduce wake deficit trends associated with varying wake overlap under baseline conditions, as well as wake deflection caused by intentional yaw misalignment during wake steering operation. Normalised velocity deficit MAE values range from 7% to 15%, with discrepancies mainly linked to inflow heterogeneity, near-wake complexity and model-specific parameterisations. Power prediction errors increase with farm depth. Model combinations incorporating cumulative wake superposition and refined turbulence formulations show improved agreement with field measurements; however, all models struggle to capture localised flow features. Normalised turbine-level power output MAE ranges from 3% to 23%, while farm-wide power output errors range between -13% and +30%. Accurate farm-level predictions may conceal compensating errors at individual turbines. Future work should focus on improved inflow characterisation and blockage effects to enhance predictive reliability.

physics.flu-dyn↗

arXiv2026

Modelling Farm-to-Farm Interaction Using a Fast Linearised Numerical Approach

This paper presents a computationally efficient, linearised numerical method for modelling aerodynamic interactions between wind farms. The linearised two-dimensional incompressible equations are solved using Fourier transforms in the horizontal direction and finite-difference discretisation in the vertical. Model predictions are validated against large-eddy simulation (LES) data, focusing on a tandem wind farm configuration where a downstream wind farm operates within the wake of an upstream array. A parametric study is then conducted to examine the impact of this wake on the performance of the downstream farm across a range of inter-farm distances and hub-height ratios. We demonstrate that the upward vertical displacement of these wakes is driven by asymmetric turbulent entrainment caused by the farm's proximity to the ground, which restricts downward wake expansion. Consequently, the results suggest that, due to this upward wake displacement, downstream wind farms with higher hub heights may be more strongly affected by upstream farms than those with lower hub heights.

physics.flu-dyn↗

arXiv2026

Analytical modelling of wind-turbine wake turbulence in neutral atmospheric boundary layers

So-called engineering or analytical wind farm flow solvers typically build upon two submodels: one for the velocity deficit and one for the wake-added turbulence intensity. While velocity deficit modelling has received considerable attention, wake-added turbulence models are less prevalent in comparison. Yet, accurate estimates of local turbulence intensity are essential for predicting flow interactions and energy yield, as turbine wakes are both sensitive to, and sources of turbulence. Existing wake-added turbulence models are typically empirical or assume axial symmetry despite the inherently three-dimensional nature of turbulent wake fields. In this work, we present a new model for wake-added turbulence intensity. Our approach is based on the analysis of the TKE and the streamwise Reynolds stress budget, incorporating classical RANS modelling assumptions and far-wake approximations. The resulting model maintains a simple and practical form, demonstrating strong agreement with LES and wind tunnel measurements. Our model provides a more physically consistent and predictive tool for wind farm flow modelling and performance estimation.

physics.flu-dyn↗

arXiv2026

Optimal wind farm energy and reserve scheduling incorporating wake interactions

This paper proposes a novel approach for optimal energy and reserve scheduling of wind farms by explicitly modelling wake interactions to enhance market participation and operational efficiency. Conventional methods often neglect wake effects, relying on power curve estimations that represent an upper limit and reduce market performance. To address this, a two-stage stochastic programming framework is developed, integrating a wake-aware power estimation model within the FLORIS simulation software. Wind and reserve uncertainties are addressed through scenario generation and reduction, enabling wind power producers to optimise participation in day-ahead energy and ancillary services markets, with particular focus on the Frequency Restoration Reserve (FRR). The wake-aware model provides more realistic power output predictions based on site-specific wind and atmospheric conditions, improving scheduling accuracy and reducing imbalance penalties. Wake steering is further employed to mitigate wake-induced losses and increase income through participation in ancillary services. The proposed approach is evaluated through a case study of the London Array offshore wind farm participating in the Great Britain (GB) electricity markets. Results show that conventional methods estimate production 12-13% higher, leading to imbalance penalties and 3% lower revenue compared with the wake-aware approach accounting for wake interactions. Moreover, the steering-enhanced approach yields an additional 1-2% increase in income relative to the wake-aware baseline. These findings underscore the value of accounting for wake interactions in wind farm scheduling and demonstrate the economic and operational benefits of active wake management, offering insights for improving grid stability and profitability as wind penetration continues to rise.

physics.flu-dyn↗

arXiv2024

Modelling turbulence in axisymmetric wakes: an application to wind turbine wakes

A novel fast-running model is developed to predict the three-dimensional (3D) distribution of turbulent kinetic energy (TKE) in axisymmetric wake flows. This is achieved by mathematically solving the partial differential equation of the TKE transport using the Green's function method. The developed solution reduces to a double integral that can be computed numerically for a wake prescribed by any arbitrary velocity profile. It is shown that the solution can be further simplified to a single integral for wakes with Gaussian-like velocity-deficit profiles. Wind tunnel experiments were performed to compare model results against detailed 3D laser Doppler anemometry data measured within the wake flow of a porous disk subject to a uniform freestream flow. Furthermore, the new model is used to estimate the TKE distribution at the hub-height level of the rotating non-axisymmetric wake of a model wind turbine immersed in a rough-wall boundary layer. Our results show the important impact of operating conditions on TKE generation in wake flows, an effect not fully captured by existing empirical models. The wind-tunnel data also provide insights into the evolution of important turbulent flow quantities such as turbulent viscosity, mixing length, and the TKE dissipation rate in wake flows. Both mixing length and turbulent viscosity are found to increase with the streamwise distance. The turbulent viscosity however reaches a plateau in the far-wake region. Consistent with the non-equilibrium theory, it is also observed that the normalised energy dissipation rate is not constant, and it increases with the streamwise distance.

physics.flu-dyn↗

arXiv2024

A fast-running physics-based wake model for a semi-infinite wind farm

This paper presents a new generation of fast-running physics-based models to predict the wake of a semi-infinite wind farm, extending infinitely in the lateral direction but with finite size in the streamwise direction. The assumption of a semi-infinite wind farm enables concurrent solving of the laterally-averaged momentum equations in both streamwise and spanwise directions. The developed model captures important physical phenomena such as vertical top-down transport of energy into the farm, variable wake recovery rate due to the farm-generated turbulence, and also wake deflection due to turbine yaw misalignment and Coriolis force. Of special note is the model's capability to predict and shed light on the counteracting effect of Coriolis force causing wake deflections in both positive and negative directions. Moreover, the impact of wind-farm layout configuration on the flow distribution is modelled through a parameter called the local deficit coefficient. Model predictions were validated against large-eddy simulations extending up to 45 kilometres downstream of wind farms. Detailed analyses were performed to study the impacts of various factors such as incoming turbulence, wind-farm size, inter-turbine spacing, and wind-farm layout on the farm wake.

physics.flu-dyn↗

arXiv2021

A vortex sheet based analytical model of the curled wake behind yawed wind turbines

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.

physics.flu-dyn↗

arXiv2021

Wake steering of multirotor wind turbines

In this paper, wake steering is applied to multirotor turbines to determine whether it has the potential to reduce wind plant wake losses. Through application of rotor yaw to multirotor turbines, a new degree of freedom is introduced to wind farm control such that wakes can be expanded, channelled, or redirected to improve inflow conditions for downstream turbines. Five different yaw configurations are investigated (including a baseline case) by employing large-eddy simulations (LES) to generate a detailed representation of the velocity field downwind of a multirotor wind turbine. Two lower-fidelity models from single-rotor yaw studies (curled-wake model and analytical Gaussian wake model) are extended to the multirotor case and their results are compared with the LES data. For each model, the wake is analysed primarily by examining wake cross sections at different downwind distances. Further quantitative analysis is carried out through characterisations of wake centroids and widths over a range of streamwise locations, and through a brief analysis of power production. Most significantly, it is shown that rotor yaw can have a considerable impact on both the distribution and magnitude of the wake velocity deficit, leading to power gains for downstream turbines. The lower-fidelity models show small deviation from the LES results for specific configurations; however, both are able to reasonably capture the wake trends over a large streamwise range.

physics.flu-dyn↗

arXiv2020

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.

physics.flu-dyn↗