Data assimilation for wake-wake interactions

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 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 the University of Sheffield. The project is part of a Research Cluster focusing on Predicting Offshore Wind wake interactions for Energy and enviRonment (POWER).

Large scale wind farms often consist of hundreds of wind turbines with diameters going up to hundreds of metres. The wakes generated by these turbines interact with each other. The accurate modelling of the interaction between the wakes can have significant impact on our ability to optimise the operations of large wind farms and maximise their energy output.

Different modeling approaches exist. Semi-analytical wake models offer efficient estimates of key features, while high-fidelity simulations like Large Eddy Simulations (LES) provide detailed 3D turbulence information, often used to understand the underlying physics and calibrate simpler models.

Recently, research has focused on controlling wind farms for power generation optimisation. For example, adjusting the yaw angle of turbines has been shown to increase power output by up to 17%. However, these control strategies introduce unsteady modulations into the wakes. This unsteadiness poses a new challenge for LES and other models. For instance, standard models struggle to accurately simulate wakes under active yaw control, and the prediction of power output suffers as a consequence.  As a recent review highlighted, “Computational approaches that enable higher-fidelity representations under the rapidly changing behaviour of a controlled wind farm remain an ongoing challenge.”

The core scientific question is how to model or parameterise these non-equilibrium wake features (introduced or amplified by the controls). This project addresses this question using a data-driven approach, leveraging the growing availability of wind tunnel and field data. The goal is to combine data assimilation (DA) techniques with LES to improve our understanding and prediction of wake-wake interactions. The application of DA within LES is a relatively unexplored area, with many open questions. This project consists of several interconnected objectives:

1) We will evaluate the limitations of current LES models when simulating actively controlled wind farms.

2) To enable effective and consistent synthesis between data with LES, we will investigate the sensitivity of the wakes with respect to flow data, and develop methods for data enrichment or reduction if necessary.

3) We will develop methods based on the ensemble Kalman filter (EnKF) to improve both the modelling of small-scale turbulence and the overall LES predictions of unsteady wake interactions

Methodology

The project will involve:

1) conducting large eddy simulation of wind farms [6];

2) parametrisation of subgrid-scale physics (e.g. [7, 9]);

3) innovative applications of data assimilation techniques including Ensemble Kalman Filter and variational methods [8] with LES as the state model;

4) developing adjoint-based sensitivity analysis to assess the significance of the experimental or field data for data assimilation. (e.g. [8])

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.

In addition, the successful candidate will also develop skills in:

1. High performance computing
2. Numerical simulations
3. Modelling
4. Data analytics
5. Numerical optimisation
6. Fluid dynamics

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, mathematics or statistics, we would like to hear from you.

If you have any queries about this project, please contact Dr Yi Li, yili@sheffield.ac.uk

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

Watch our short video to hear from Aura CDT students, academics and industry partners:

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

Our funded Doctoral Scholarships are available to UK Students. The advertised CDT scholarships in this current recruitment round are available to Home (UK) Students only as the CDT has reached the annual cap, set by the funding council (UKRI EPSRC), on international student recruitment for the 2025 intake. 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).

Guaranteed Interview Scheme 

The CDT is committed to generating a diverse and inclusive training programme and is looking to attract applicants from all backgrounds. We offer a Guaranteed Interview Scheme for home fee status candidates who identify as Black or Black mixed or Asian or Asian mixed if they meet the programme entry requirements. This positive action is to support recruitment of these under-represented ethnic groups to our programme and is an opt in process. 

Find out more 

How to apply

Please ensure that you familiarise yourself with the Aura CDT website before you apply to give you a good understanding of what a CDT is, our CDT’s research focus and the training and continuing professional development programme that runs alongside the CDT. The Frequently asked questions page and Candidate resources page are essential reading prior to applying.  

Applications are open until Friday 9 May 2025 

Applications to this project are made via the University of Sheffield admissions system. If you have not applied to the University of Sheffield before, you will need to set up an account to enable you to track the progress of your application and upload supporting documents.  

Follow this link to apply for CDT projects at the University of Sheffield:   

https://www.sheffield.ac.uk/postgraduate/phd/apply/applying  

With your application, you need to upload copies of the following supporting evidence:  

• Complete transcripts (and final degree certificate(s) where possible). If your qualification documents are not in English, you will need to supply copies of your original language documents as well as their official translation into English.  
• Your Curriculum Vitae (CV).   
• A completed Supplementary Application Form (upload when asked for your Supporting Statement).  

Please download the Supplementary Application Form here. 

Ensure you complete all sections of the Supplementary Application Form in font and size Calibri 11pt, specify the research project you are applying for.  

Uploading the form 

When you have completed the form, please save it as a pdf format and labelled as follows: 

Last name_first name PhD application form 

Our support team will then process the form removing your name and allocating you a number prior to your application being assessed. 

Upload the form as part of your application documents through the University of Sheffield student application portal, when asked to add your Supporting Statement. The Form replaces the Supporting Statement and so you do not need to complete the Supporting Statement section. Please do not send your form directly to the Offshore Wind CDT.   

Interviews will be held online with an interview panel comprising of project supervisory team members from the host university where the project is based.  Where the project involves external supervisors from university partners or industry sponsors then representatives from these partners may form part of the interview panel and your supplementary application form will be shared with them (with the guaranteed interview scheme section removed). Interviews will take place during early and mid-June. 

If you have any queries about this project, please contact Dr Yi Li, yili@sheffield.ac.uk

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

References & Further Reading

[1] Meneveau, 2019, Big wind power: seven questions for turbulence research, Vol. 20, J. Turb.

[2] Bastankhah et.al, 2021, Analytical solution for the cumulative wake of wind turbines in wind farms, Vol. 911, J. Fluid Mech.

[3] Shapiro et.al, 2022, Turbulence and Control of Wind Farms, Vol. 5, Annu. Rev. Control Robot. Auton. Syst.

[4] Bastankhah and Porte-Agel, 2019, Wind farm power optimization via yaw angle control: A wind tunnel study, Vol. 11, J. Renewable Sustainable Energy.

[5] Munters and Meyers, 2018, Dynamic Strategies for Yaw and Induction Control of Wind Farms Based on Large-Eddy Simulation and Optimization, Vol. 11, Energies.

[6] Porte-Agel, F. et.al, 2020, Wind-Turbine and Wind-Farm Flows: A Review, Vol. 174, Boundary-Layer Meteorology.

[7] Li, Y. et.al, 2006, Subgrid-scale modeling of helicity and energy dissipation in helical turbulence, Vol. 74. Physical Review E.

[8] Li, Y. et.al, 2020, Small-scale reconstruction in three-dimensional Kolmogorov flows using four-dimensional variational data assimilation, Vol. 885, J. Fluid Mech.

[9] Lin, M. and Porte-Agel, F., 2022, Large-eddy simulation of a wind-turbine array subjected