# Opportunities to join the Waves Group

We normally take one or two new research students each year. They would usually have a first class undergraduate degree in mathematics, physics or engineering, and usually take Part III, although Part III may not be strictly necessary. Unless otherwise indicated, funding is provided through the department, as detailed here and here. Please note the required qualifications and deadlines given on those pages.

# Ph.D. projects

## Jet-noise control via serrated nozzles

Noise generated within aeroengines propagates through both the bypass duct and jet nozzle and is scattered by these edges. Some modern jet engines now implement serrations on these trailing edges in an attempt to reduce scattered noise. These designs can vary greatly as no optimal serration has been determined.

This project will make use of analytical methods to determine the far-field noise scattered by a serrated trailing edge of a cylindrical duct, then use this solution to optimise the edge geometry for maximum noise reduction. Both hard-wall and acoustically soft-wall (impedance) conditions will be investigated.

This project will be supervised by Lorna Ayton.

## Spanwise variable leading-edges, and Wiener-Hopf factorisation of structured matrices

Aeroacoustic noise is generated when unsteady turbulence impinges on the leading edge of aerodynamic structures, such as during the so-called blade-blade interaction of rotor blade wakes impinging on stator blades within an aeroengine. Redesigning the leading edge of the stator blades can lead to large interaction noise reductions. This project will use sophisticated techniques from complex analysis to tackle the leading-edge noise problem when there is variability in design in the spanwise direction. The scattering problem leads to structured Wiener-Hopf equations, however the factorisation of a Wiener-Hopf kernel, K, into two parts K=K+K-, where K+ and K- are analytic in complementary regions of the complex plane respectively, is incredibly difficult to do exactly.

Through iterative algorithms or approximation methods, you will develop new techniques to factorise these structured matrices, and hence produce important acoustic results for new designs of aerofoils that are appropriate for use in aeroengines.

This project will be supervised jointly by Anastasia Kisil and Lorna Ayton.

## Noise generated by aerofoils in high speed flow

A key component to aeroengine noise arises from the interaction of unsteady blades shed by rotor blades interacting with downstream stator blades, in a process often called turbulence-aerofoil interaction, or gust-aerofoil interaction. In flows with moderate Mach numbers of less than 0.8 the generation of this noise is well understood from both an analytical and numerical perspective. High-performance aeroengines however operate with flow speeds approaching or exceeding the speed of sound. In these cases, shock waves will have a significant effect on the acoustic field.

This primarily theoretical project will develop an asymptotic solution for gust-aerofoil interaction noise in high-speed flows to understand the effects of shocks on the acoustic field.

This project will be supervised by Lorna Ayton.

If none of these projects are of interest, why not email Nigel Peake, Mark Spivack, or Lorna Ayton to see if they have anything else lined up?

# Postdoctoral projects

Postdoctoral positions will be advertised here as and when they become available.