Analytical approaches to the modelling of multi-row turbine arrays

Thesis

The increasing recognition of wind turbines as an effective source of renewable power generation that can deliver a net zero carbon future, has led to the construction of larger turbine arrays. Predicting the performance of large turbine arrays requires consideration of many physical factors, such as array geometry, turbine operation, inflow conditions and turbulent wake mixing. Due to the large parameter space that an array may be optimised over, low-order models with low computational cost are often employed. This thesis is concerned with the extension of one of those low-order models; the hybrid inviscid-viscous model of multi-row turbine arrays.

The first extension presented is to the inviscid portion of the model by generalising the linear momentum actuator disk theory, such that the system with non-uniform inflow may be analytically solved utilising a single cubic equation. The impact of shear on a single turbine is then explored, followed by an analysis of a multi-row turbine, which indicates possible performance gains due to varying turbine resistance at each row.

The second extension is in the construction of a novel wake mixing model based on the momentum deficit and self-similarity of Reynolds stresses. This self-similar mixing model is then compared with the results of a "uniform" mixing model. It is shown that the predictions made by each model are similar when the mixing rate parameterised in the uniform model is accurate for a given turbine resistance and array configuration.

The final extension presented in the thesis concerns itself with “anisotropic blockage”, in which a turbine is not equidistant from all nearby boundaries or lines of symmetry with other turbines. A range of Reynolds-averaged Navier-Stokes (RANS) simulations are conducted, followed by a new theoretical method of estimating the turbine efficiency based on scale-separation arguments. This method is benchmarked against an existing "isotropic blockage" model and is found to agree better with the RANS simulations.

Authors: Juniper, M

• DOI: 10.5287/ora-eqjx0aqar
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: tidal energy; wind energy
• Subjects: Fluid Dynamics