This project centres on finding mathematical solutions to complicated fluid-structure interaction problems, bringing together a variety of advanced mathematical techniques to solve key problems in the aerospace industry, such as reducing aircraft noise. Excessive environmental noise from airports and wind farms is a key issue affecting both public health and the expansion of the aviation and sustainable energy industries.

A current expanding area of research in aeroacoustics is in leading-edge (at the front) and trailing-edge (at the rear) adaptations to standard blades on aeroplanes or wind turbines. It is believed that these adaptations can lead to significant decreases in generated noise and are largely inspired by nature, in particular the silent flight of owls. It is well known that owls are unique among birds in that they fly almost silently. This is believed to be possible due to a number of features their wings possess which are not present in other species. By creating new designs aimed at mimicking these owl-like features, this project shall attempt to significantly reduce noise generated by aircraft and wind turbine blades.

A primary source of noise generated by aeroengine blades is leading-edge noise, arising from the interaction of an unsteady fluid with the front of the solid body. Conversely, trailing-edge noise is a dominant contributor to airframe and wind turbine noise, arising due to the interaction of turbulence above the blades with the rear of the blade (the trailing edge).
Understanding and quantifying the mechanisms generating these different types of noise is vital to knowing what adaptations can be made to current designs in order to reduce the overall sound emitted by these systems. Potential noise reduction designs include; blades with serrated, or porous and flexible trailing edges, or fringed leading edges. Research into the effectiveness of these designs is typically experimental or numerical, which cannot delve deeper in to the results to tell you why such a design is effective, merely if it is or not. This project ultimately aims to provide the answer to why.

Mathematical solutions derived using analytic methods can be incredibly powerful as they preserve the vital physics of these fluid-structure interaction problems, but significantly reduce computational costs and can address cases in which numerical models struggle, such as generation of high-frequency noise. The speed of mathematical predictions can identify important areas that require further investigation, giving a head start to developing new noise-reducing or increased-performance technologies.

Through mathematical analysis, this project will give insight into the mechanisms by which these adapted leading- and trailing-edge designs reduce noise, and obtain relationships between key design features, such as the porosity of a trailing-edge adaptation or original blade geometry, and the total noise reduction, allowing for quick optimisation of the design without the need for large numbers of experiments or costly computation.

Potential Impact:
This project is heavily inspired by industrial and environmental concerns, principally in the aviation and sustainable energy sectors. The direct impact of this research on society will stem from the engineering applications of the mathematical investigations, and the strong collaboration between myself and engineers around the world developing new aerodynamic designs.

Worldwide the aviation industry is growing, and for Heathrow alone, the Airports Commission predicts up to £211bn in economic benefits and 180,000 jobs to the UK from an expansion [1]. With rapidly growing demand for air transport it is imperative to take steps to reduce the environmental impact of emissions and noise pollution. Unwanted noise is a key public concern and continual restrictions are placed on take-off noise levels; the Advisory Council for Aerospace Research in Europe (ACARE) set targets in 2001 to reduce perceived noise levels by 50% by 2020, which have been extended in the new Flightpath 2050 vision to a reduction of 65% (relative to noise levels in 2000) by 2050 [2]. New technologies capable of noise control and reduction must be developed to achieve these goals to allow companies, such as UK-based Rolls Royce who employ over 50,000 staff, to remain competitive in the global aviation market without adversely impacting profits.

Unwanted noise also restricts the expansion of wind farms. In this situation it is often not the level of perceived noise (i.e. loudness) that causes complaints, but the repetitive nature of the noise which causes annoyance. Currently many wind turbines are braked to reduce noise, leading to up to a 25% power reduction; new noise control technologies could improve power output without increasing noise levels.

Environmental noise is linked to a variety of health problems, including high blood pressure and cardiovascular disease, cognitive impairment in children, and sleep disturbance. Combined these health problems are predicted to lead to over 1 million healthy life years lost each year in Western Europe [3]. Noise is not just a nuisance for the public, but a serious health concern, and hence reducing environmental noise from airports and wind farms will have great benefits for public health and well-being.

During the project I will supervise a PhD student (funded by the department), who will become a highly-trained aeroacoustician/aerodynamicist. This training is of direct value to the academic community, or the wider R&D industry in the UK as there is an established connection between DAMTP (Department of Applied Mathematics and Theoretical Physics) and Rolls-Royce through the University Gas Turbine Partnership (UGTP)

New mathematical techniques will be disseminated to the academic community through regular journal publications and conference presentations, whilst new noise reduction technologies will be developed and disseminated with my collaborators to industry; the UGTP in Cambridge links to Rolls-Royce, whilst the Airbus Noise Technology Centre in Southampton allows direct dissemination of research from academia to Airbus.

To summarise, the development of new mathematical techniques will have a direct impact in academia in various research areas (as discussed in the Academic Beneficiaries section). The applications of these mathematical methods has the potential to improve the quality of people's lives through environmental impact and has commercial importance by potentially safeguarding jobs and promoting expansion in the scientifically-driven aviation industry.

[1] European Commission. "Flightpath 2050: Europe's Vision for Aviation" Report of the High Level Group on Aviation Research, Publications Office of the European Union, Luxembourg (2011)
[2] Airports Commission "Airports Commission: final report" Independent report of the Airports Commission, UK, (2015)
[3] World Health Organisation "Burden of disease from environmental noise" European Commission (2011)