Much of the research in The School of Mathematics is inspired by problems arising in industry, engineering and many other scientific fields.
This can be to try and understand why certain industrial processes or devices do not work, or to improve current models used by industry to predict the efficiency, integrity and safety of their products.
Members of the School of Mathematics who conduct research in this area are: Mark Blyth, Mark Cooker, Paul Hammerton, Alexander Korobkin, Emilian Parau, Richard Purvis, Nigel Scott, and Robert Whittaker. These researchers have a wide range of modelling experience. Details of some of the past and present projects are included below.
Ditching of aircraft and ship slamming
Research Team: Alexander Korobkin, Mark Cooker, Richard Purvis
These two closely related projects are funded via the EU, SMAES (ditching) and TULCS (slamming). This work aims to develop a mathematical description of the violent water flows that occur after the relatively high-speed impact of a solid body into water (a ship slamming into rough seas, or an aircraft landing on water in an emergency). The object is to predict the complicated fluid-structure interaction that occurs as a body impacts at speed into water. A major objective is to predict the total force that the body is subjected to, and thereby assess whether the design is strong enough to withstand such an incident. Full numerical models of the process fail to accurately predict the behaviour at impact due to the small time scales and enormous forces present and these projects look to add theoretical understanding and predictions to improve industrial models. This in turn should lead to improved design and testing of both ships and aircraft during violent impact events. Both of these projects are closely linked with a number of industrial partners.
Research Team: Mark Cooker
Understanding how waves break against a seawall, and particularly how much force (or potential damage) they impart is a crucial part of designing effective and lasting sea defences. Across many areas of the UK and beyond, effective sea walls are crucial to protect areas of human habitation, as well as farming and conservation areas, from tides and wave motion. The seawall is designed to reflect the energy in the wave back out to sea but must be carefully constructed to ensure the wall, and any other structures attached to it, can cope with large amount of energy contained in each wave impact. Mathematical models have been developed to predict the typical loads experienced by the wall, and current work is looking at how cracks in a seawall can be exacerbated by wave impact. Understanding how the sand at the base of the wall is scoured (or eroded) away is also important.
Breaking wave approaching Cromer beach
Droplet impacts and aircraft icing
Research Team: Richard Purvis
When flying through cloud at or below freezing, aircraft can accrete ice on all forward facing components, most crucially on the leading edge of a wing or tail, around the engine intakes and on the rotor blades of a helicopter. Supercooled water droplets suspended in the cloud impact upon the aircraft. After impact, dependent on many factors such as temperature, droplet size and speed, this water then spreads and freezes. The resultant ice can build up quite quickly and can have serious consequences with large increases in drag and decrease in lift, leading to a severe detrimental effect on the stability, control and safety of an aircraft. Modelling at UEA, along with colleagues at Cranfield and UCL, is trying to understand how droplet impacts and subsequent splashing influence the ice build up as, particularly for larger droplets, existing models tend to poorly predict the ice build up and this is mostly attributed to splashing. As well as examining droplet impact dynamics, other research areas include pre-impact air cushioning and droplet distortion.
Two examples of aircraft icing: Left on a wing and right on a propeller.
Images from the NASA Glen website.
Research Team: Mark Cooker, Richard Purvis, Robert Whittaker
Maths-in-Industry study groups are week-long workshops initiated by the University of Oxford in 1968, and provide a forum for industrial scientists to work alongside academic mathematicians on problems of direct industrial relevance. At each Study Group, mathematicians from around the world gather to work intensively on problems brought by outside companies. The problems can come from a variety of areas, including: fluid mechanics, chemistry, electronics, engineering, transport, environment, finance, optimisation, biology and medicine.
The School of Mathematics hosted the 85th European Study Group with Industry in 2012, and members of the School have wide experience of attending and participating in these events. These have included working on problems as diverse as designing a green roof for Ireland, predicting diver positioning using mobile phone technology, The effects of friction and compression on explosives, efficient silicon melting, and blown polysilicon fuses.