The project investigates developments of helical vortices shed from tips of wind turbines and ubiquitously observed in offshore wind farms. The instabilities and breakdown of these vortices are critical to the development of the wake flow and consequently impose significant impacts on downstream wind turbines in terms of fatigue loading, lifetime and acoustic noise. Better understanding of the dynamics of helical vortices will lead to more advanced methods in wind turbine design and wind farm layout, more accurate predictions of wind turbine lifetime and energy generation of wind farms, and ultimately reduced price of wind energy. A better understanding of the dynamics of helical vortices will also be more generally useful, e.g. in aerodynamic performance of helicopter rotors or turbine impellers, erosion induced by tip-vortex cavitation in ship propellers, and breakdown of straight vortices.

At present there are no general numerical tools to calculate the global stability of helical vortices and the breakdown of these vortices driven by instabilities. Most of the existing work on helical vortices concerns experimental measurements of vortex breakdown or analytical stability analyses using simplified models, e.g. inviscid and thin helical vortex filaments perturbed by either short or long waves. As a result, the path to understanding the role of instabilities in breakdown is blocked, and so also is the capability to design wind turbines and farms taking into account the effect of wake flow on performances.

General numerical studies of global stabilities of helical vortices require a novel algorithm originating from classical stability theories, which have been used on straight vortices in both Cartesian and cylindrical frames. Such an algorithm to study helical vortices will be implemented in the Frenet frame, taking advantage of the homogeneity of the helical vortices in the vortex axis direction and therefore enabling the integration of existing stability theories across scales (from short-wave to long-wave) into one framework. Both theoretical models of helical vortices and experimentally measured mean flow in the wake of a turbine will be used as the base flow in stability studies. The results will be cross-validated against field measurements and theoretically derived instabilities.

Direct numerical simulations (DNS) of helical vortices initially perturbed by the most energetic modes will be conducted in the Frenet frame, which enables DNS at much larger Reynolds numbers than other frames. The simulations will reveal the role of various linear modes in the breakdown of helical vortices. The distribution of wind in the wake extracted from the simulation can be modeled as a more accurate alternative of the models used in current industry applications, e.g. the PARK model. This new model will be broadly useful in the design and operation of large-scale offshore wind farms, which require fast & precise predictions of the wake flow.

Potential Impact:
The proposed research will offer the opportunity to strengthen the international leading position of the UK in the area of hydrodynamic stabilities and wind turbine aerodynamics. Since the research will ultimately reduce the price of electricity generated by wind farms, the UK economy will also benefit from this research, considering that the UK has some of the best wind resource in Europe and plans to expand the current offshore wind energy by over ten fold by 2030. In addition, the topic also responds to the need of more adventurous research in the energy field to meet the 2050 carbon-emission targets of the UK.

The outcome will be particularly useful to the wind energy industry, as well as to other industries involving products where helical vortices have the potential to affect aero/hydrodynamic performances. The impact of the techniques developed in the proposed research to industry, especially the companies managing large-scale offshore wind farms, will consist of the following aspects.

a) Design of wind turbines. Understanding the mechanisms of instabilities and non-normality identified in this project will shed light on the design of aerodynamic configurations of wind turbines in terms of promoting instability and breakdown and reducing interactions between turbines. The computed wind speed fluctuation associated with helical vortex breakdown is related with fatigue loading on downstream turbines and consequently the structural design of turbines.

b) Optimal layout of wind farms in accordance with the computed distribution of the mean wind velocity and velocity fluctuations, so as to reduce interactions of wind turbines.

c) More precise estimation of wind power generation, taking into account of the wake effects. Current wind power is estimated mainly based on meteorological data and the details in the wake flow are neglected. In this project an analytical model or database of wind distributions in wind farms will be extracted based on the proposed large-scale numerical simulations.

d) The numerical code developed in this project. This programme can be used in the design or maintenance of offshore wind farms to evaluate effects of helical vortices in the wake. It is noted that the programme may generate intellectual property.

e) All the above impacts will ultimately contribute to reducing the price of electricity generated by wind farms.

The impact of this project to the academic community of fluid mechanics will consist of the following aspects.

a) Stability tool that unifies the current theories on helical vortex stabilities based on various assumptions. The theoretically predicted instabilities and distributions of unstable modes can be validated in the proposed research.

b) Effects of noise outside the vortex core. This periphery noise has been shown to induce vortex meandering in straight vortices, but has not yet been actively investigated in the context of helical vortices. This type of noise physically originates from environmental turbulence and can be numerically studied through non-normality analyses.

c) The gap between helical vortex instabilities and helical vortex breakdown will be filled by direct numerical simulations of vortex flow perturbed by the most energetic modes, so as to identify the role of linear modes in vortex breakdown.