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

Project Description:

This PhD scholarship is offered by the EPSRC CDT in Offshore Wind Energy Sustainability and Resilience; a partnership between the Universities of Durham, Hull, Loughborough and Sheffield. The project is sponsored by the industry partner, the Offshore Renewable Energy (ORE) Catapult. The successful applicant will undertake six-month of training with the rest of the CDT cohort at the University of Hull before continuing their PhD research at Durham University.

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number of wind farms – particularly offshore in Northern Europe) has meant that this empirical approach is now outdated and predictions/optimisation based on such empiricism is unreliable and crucially, becoming ever more unreliable.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:

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

The following are the specific research objectives (ROs) of the project that follow from these aims:

• RO1. Calibration of our existing, two-dimensional physics-based model for an infinitely large wind farm in the spanwise direction.
• RO2. Development, and calibration of our physics-based model for a finite span wind farm.
• RO3. Validation of our physics-based model on a representative cluster of wind farms.
• RO4. Dissemination of our work to a worldwide audience to generate maximum impact; this will include both academic and industrial dissemination.

Training and Development

You will benefit from a taught programme, giving you a broad understanding of the breadth and depth of current and emerging offshore wind sector needs. This begins with an intensive six-month programme at the University of Hull for the new student intake, drawing on the expertise and facilities of all four academic partners. It is supplemented by Continuing Professional Development (CPD), which is embedded throughout your 4-year research scholarship.

Dependent on the successful candidate’s experience, there will opportunity to attend specific post-graduate level modules in areas such as fluid dynamics, aerodynamics, robotics.

Entry requirements

If you have received a First-class Honours degree, or a 2:1 Honours degree and a Masters, or a Distinction at Masters level with any undergraduate degree (or the international equivalents) in engineering, we would like to hear from you.

If your first language is not English, or you require Tier 4 student visa to study, you will be required to provide evidence of your English language proficiency level that meets the requirements of the Aura CDT’s academic partners. This course requires academic IELTS 7.0 overall, with no less than 6.0 in each skill.

If you have any queries about this project, please contact Dr Majid Bastankhah (majid.bastankhah@durham.ac.uk).

You may also address queries about the CDT to auracdt@hull.ac.uk.

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Funding

The CDT is funded by the EPSRC, allowing us to provide scholarships that cover fees plus a stipend set at the UKRI nationally agreed rates. These are currently circa £19,795 per annum at 2025/26 rates and will increase in line with the EPSRC guidelines for the subsequent years (subject to progress).

Eligibility

Research Council funding for postgraduate research has residence requirements. Our CDT scholarships are available to Home (UK) Students. To be considered a Home student, and therefore eligible for a full award, a student must have no restrictions on how long they can stay in the UK and have been ordinarily resident in the UK for at least 3 years prior to the start of the scholarship (with some further constraint regarding residence for education). For full eligibility information, please refer to the EPSRC website.

We also allocate a number of scholarships for International Students per cohort.