Development and validation of physics-based models for wakes of large offshore wind farms

Project Description:

This Research Project is part of the Aura CDT’s Predicting Offshore Wind wake interactions for Energy and the enviRonment (POWER) Cluster.

Interaction between adjacent offshore wind farms, due to their wakes impinging on one another, is increasingly becoming a crucial and timely research topic. To meet new ambitious targets for offshore wind in the UK, many new wind farms are expected to be installed in promising geographic areas offshore; those limited areas that yield strong and predictable winds sufficiently close to centres of population such as the North Sea. In addition to technical challenges, these farm-to-farm wake interactions may even provoke legal and financial conflicts between operators of neighbouring wind farms. Therefore, accurate modelling of wind-farm wakes is crucial for optimisation of future wind energy projects in an increasingly competitive offshore environment.

High-fidelity numerical simulations, e.g. LES, that are often used in academic research are computationally expensive and difficult to use for planning purposes and industrial applications. Simple analytical modelling is therefore essential for the wind-energy industry, since wind-farm optimisation requires numerous evaluations of a merit function (rewarding overall power production and penalising exposure to fatigue damage/maintenance). Further, given that the generation of wind energy is by its very nature a multidisciplinary engineering challenge the basis of the aerodynamic modelling should be simple as it is only one facet of the problem. Simple models have existed for some time, since at least the 1980s, but these have been based on empiricism. The rapid technological growth of the wind-energy sector in recent years (ever larger turbines, ever larger wind farms, an increasing number of wind farms – particularly offshore in Northern Europe) has meant that this empirical approach is now outdated and predictions/optimisation based on such empiricism is unreliable and crucially, becoming ever more unreliable. In particular, with the ever-increasing deployment of offshore wind power stations it now becomes imperative to model the wakes of wind farms themselves since the wake of one wind farm now becomes the inflow to the next.

The wake of a wind farm is subjected to physics that cannot be simply derived from knowledge of the effects of individual turbines, primarily due to the question of scale. Satellite images show that the wakes of offshore wind farms last for many kilometres and the relevant physics include:

• the Coriolis force due to the rotation of the Earth,
• the cumulative effect of multiple wind-turbine wakes,
• large-scale entrainment physics from the atmospheric turbulent boundary layer.

We have developed a first iteration of such a physics-based model for the prediction of the evolution of wind-farm wakes of infinite span. The model is based on the Reynolds-Averaged Navier-Stokes (RANS) equations, written in a rotating frame such that a Coriolis forcing term is included (Bastankhah et al. 2023). The closure problem of turbulence requires modelling assumptions to be made (for the Reynolds stress terms and pressure velocity coupling) and further assumptions/simplifications are then made subsequently in order to streamline the model into a tractable, inexpensive form that can be used for design calculations.

Our model shows great promise in its ability to predict the evolution of wind-farm wakes based on comparison with high-fidelity simulations (i.e., LES data), however work remains to be done in order to improve it. This requires high-quality data against which to calibrate the various model coefficients, a critical review of all the assumptions made (making improvements where necessary), and ultimately extension of the model to incorporate the effect of the finite-span of the wind farm (and hence lateral entrainment into the wake in addition to vertical entrainment). The aims of the current proposal are thus:

1. To obtain the high-quality data necessary to calibrate the existing model such that it can be implemented into existing wind-farm design tools;
2. Further development of the model to account for realistic, finite-sized wind farms, iii) calibration and validation of this updated, realistic model for real-world applications.