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

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.

Models of different levels of fidelity are developed in parallel to model wake-wake interactions. Novel semi-analytical wake models provide efficient estimate of the key mean features. High-fidelity simulations such as large eddy simulations (LES) can provide highly resolved three-dimensional turbulence, which are often used to understand the underlying physicsof the flows and to provide detailed databases for the calibration of engineering models.

Some recent research has focused on controlling wind farms for power generation optimisation or power tracking, as wind energy gradually becomes main source of electric power. For example, Bastankhah and Porte-Agel show that yaw angle control can increase power by 17%. However, the control algorithms often introduce additional unsteady modulation to the wakes. For example, it was found by Munters and Meyers that the optimal yaw and induction control strongly oscillates in time. To capture accurately the impact of the unsteadiness is the new challenge for large eddy simulations as well as other modelling approaches, which has not been fully accounted for. For example, Lin, M. and Porte-Agel, F. shows that the usual ADM and ALM models perform poorly in simulations with active yaw control. More generally, as stated in the recent review by Shapiro et.al. on the topic: “Computational approaches that enable higher-fidelity representations under the rapidly changing behaviour of a controlled wind farm remain an ongoing challenge”.

The scientific question behind these new challenges is how to model or parametrise the non-equilibrium features in the wakes (which in this case are introduced or amplified by the controls). This question has long been at the core of wind farm modelling and is one of the main questions being addressed by this cluster. This project intends to focus on a data driven approach, taking advantage of the availability of wind tunnel as well as field data that have been accumulated rapidly. The aim is to synthesise data assimilation (DA) techniques with LES to develop a modelling approach that will improve the understanding and prediction of wake-wake interactions. The application of data assimilation in the context of LES has received only limited research; many questions remain open. The project is composed of several inter-connected objectives.

1. Assessing the deficits of current LES models in the simulations of controlled wind farms.
2. In order to effectively and consistently synthesise data with LES, we will investigate the sensitivity of the wakes with respect to the data. Data enrichment or reduction might be necessary.
3. Developing ensemble Kalman filter (EnKF) based methods to improve subgrid-scale modelling as well as LES prediction for unsteady wake-wake interactions.

Methodology

Outline the different methodologies that the project will adopt and develop. Be as specific as possible and provide references for further reading.
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])

Further Queries

If you would like more information about this project, please let us know by emailing auracdt@hull.ac.uk.

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 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 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

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.

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