The UK government made it clear in a recent white paper of 2008 that nuclear energy was a vital part of the UKs energy mix to ensure both security of supply and a commitment to reduction in CO2 emissions. The recent Office of Nuclear Regulation Weightman report on the Fukushima accident has confirmed that Fukushima showed no reason to curtail nuclear operation or nuclear new build in the UK and in 2012 it is expected that EDF will start work on the first new nuclear power station at Hinkley Point. Perhaps one key issue/lesson learnt from the Fukushima accident, especially in Japan, was the need for continued research into nuclear safety to support existing and new build nuclear power plant programmes. Until recently there has been relatively little UK research into nuclear power and as such there are also relatively few young academics truly in the field. There is also a growing need to train new young talented engineers and physicists in nuclear engineering disciplines if the new build programme is to be successful and to help rebuild the UKs reputation as a world leader in this field. This proposal is made to try to address some of these issues and at the same time explore a new growing area of modelling, known as peridynamics, with great potential for modelling many problems within the nuclear engineering materials area. The project aims to investigate two nuclear fuel problems thus far difficult to model: pellet-cladding interactions (PCI) in nuclear fuels and oxide phase change/spallation on zirconium alloy cladding of water-cooled reactors. These problems are ideal for a mixed finite element (FE) -peridynamics modelling approach. Both PCI and oxide growth and spallation require a model that is able to deal with a ductile material (cladding) bonded to a brittle material (UO2 ceramic fuel) under complex stress states, geometries and incorporating heat transfer and material heterogeneity. The peridynamics approach is able to model material with defects without some of the numerical issues inherent within the FE approach. However, combining the two modelling techniques can bring the advantages of both techniques together. This project will develop a peridynamics implementation into the finite element code Abaqus. The models will then be developed further to model the specific problems of PCI and oxide spallation problems described. The project will also develop a new young post doctoral researcher and a early career academic in the field of nuclear fuel modelling.

The practical problem which this proposal addresses is how to manage the UK energy system in a future where there will be much more use of unpredictable energy sources (wind, solar) and also of inflexible energy sources (biomass, tidal, nuclear, geothermal). Wind power is highly unpredictable - effectively a random walk over lead times up to 12 hours - and the total UK output of wind power can vary unpredictably by 25% over four hours. This is the capacity of several large thermal generators, but it also takes four hours to warm up such a generator.With the government's planned extensive use of wind, for the first time ever the UK's available supply of power over the next four hours will be less predictable than the demand for it. There will be large continuous uncertainty in real time, and it is unlikely that gas generators (which will be a smaller part of the total system) can ramp fast enough to compensate for any shortfalls. Otherwise the system must use some mix of: fast-ramping but inefficient gas generators; energy storage by producers and users, and perhaps more frequent power outages, and/or wastage of temporary power surpluses.The energy industry has no standard mathematical tools for even addressing this problem. Conventional models for scheduling and storage make little allowance for uncertainty, and they tend to simplify the problem to large discrete chunks of capacity and time, in steps from one to six hours, and they also omit many engineering constraints. The fall-back tool for modelling in greater detail is simulation, but our work has shown that this gives a coarse approximation, which is unacceptably slow to compute. What is needed are mathematical models which assume continuous time uncertainty, can implement complex engineering and other constraints, and generate optimal decisions in that environment.Financial mathematics has a ready-made tool kit for modelling optimal decisions about stochastic physical systems, if we simply reverse the role of the random walk variable, from modelling a price to modelling a physical quantity. This opens a huge arsenal of tools for treating mixed deterministic and stochastic physical systems under complex constraints. The methods are as flexible as the related (partial differential) equations used to model deterministic systems in physical engineering, but this new approach turns out to be one billion times faster than corresponding simulation computations. For three years we have explored this new approach with promising results, but we have so far accepted a constraint that our models can be either complex and stochastic in price behaviour, but simple in physical behaviour (as in finance, where the most complex physical decision tends to be the binary one of buying or not buying a share) or complex and stochastic in physical behaviour, but simple in price behaviour (as in our early models, where complex flows take place into and out of a storage system, but with a deterministic price structure for fuel, which is realistic if gas has been bought on a long term contract).This proposal aims to build models in which there are complex real time disturbances to both prices and physical rates. This breaks new mathematical modelling ground, and also opens a wider class of economic applications. For example because electricity is widely traded, such models might offer a unified framework for optimal decisions on how to operate a physical electricity or storage plant, how and when to sell its output forward, and when to trade in the market without intending to deliver electricity. Finally, since the models assume a richer continuous time framework than most existing trading or engineering systems permit, the models may suggest directions for improving the working and efficiency of markets, and the physical design and evolution of electricity plants and systems.

The efficiency, safety and reliability of a wide range of engineering systems in the energy sector rely strongly on the performance of their structural components. Increasing energy efficiencies, achieved by maximising operating temperatures, will drive down CO2 emissions and is therefore essential to meet stringent legislation and the UK's and international short and long-term energy goals. Engineering components operate under adverse conditions (stress, temperature and harsh environments) causing their degradation and failure by deformation and fracture processes. Existing energy facilities are aging beyond design life and require life extension to secure short-term energy supplies. Reliable component lifetime assessment is therefore vital to ensure safe operation. New build nuclear reactors will soon be developed and future reactors designed for very high temperature operation and superior performance. Plans are also advanced for the construction of the next generation of conventional power stations with excess operating temperatures and efficiencies. Opportunities are now emerging to exploit a novel collection of innovative techniques, at micro and macro length scales, to obtain a fundamental understanding of material failure mechanisms. These will enable advanced materials and component designs with predictable in-service behaviour, which are crucial to innovation in the energy sector and the key for overcoming the outstanding challenges.Emerging experimental techniques can now reveal the processes, and quantify the extent of deformation and damage in a material as it occurs. High-energy X-ray tomography measurements will give detailed quantitative 3D volumetric insights of damage development, coalescence and failure mechanisms in the bulk of specimens at micro-length scales, during deformation under stress at temperature. In addition, complimentary non-destructive tools will be innovated for practical monitoring of large scale component degradation. At a range of length scales, a digital image correlation technique will be used to measure 3D surface strains on various geometries, and will provide evidence of the influence of defects and material inhomogeneities due to welding processes on strain fields and their evolution with time.High performance computing now facilitates advanced models to simulate material behaviour and structural components' response under various operating conditions. Experimental results will provide the basis for validated mechanistic models of material deformation and failure behaviour, which will be developed and incorporated into 3D computational models that can also include various regions of inhomogeneous material behaviour. This novel collection of advanced experimental techniques, combined with the verified computational models, will provide new powerful tools that are essential to understand and predict component failure, advance designs and optimise their operation.Initially, power plant steels will be examined. However, the methodologies developed can be extended to a wide range of materials relevant to e.g. aerospace, heat and power generation, marine and chemical technologies. The outcomes will lead to methods for component on-line monitoring, predictive multi-scale modelling of materials' initial and through-life properties and the development of accurate assessment procedures for component lifetime predictions that leads to the required plant life extension. Social and economical benefits include minimised environmental impacts, secure supplies, reduced maintenance costs and increased safety. The close collaboration with industry (including partners British/EDF Energy and E.ON) will provide an effective knowledge transfer mechanism between industry and academia, ensure industrial relevance and provide inspiration to a new generation of researchers. This fundamental, timely research is therefore valuable across industrial sectors in addition to the scientific community.

This proposal seeks funding for a three year research programme into the back-scattering of ultrasound from rough surfaces, with specific application to the Non-Destructive Evaluation (NDE) of rough cracks. This addresses an important industrial goal: to be able to predict with confidence the reflection of ultrasound from a rough defect, at any chosen angle and frequency, which could then be used to make the case for a desired plan for inspection. The research will extend knowledge in two complementary areas: the creation of an envelope approach to predict the minimum back-scatter to be expected with confidence from a statistical description of the roughness, and the development of Finite Element modelling procedures to guarantee accurate, but efficient, modelling of the scattering from detailed representations of specific rough defects. The work will be undertaken jointly by a mathematical and an engineering team, both at Imperial College. The proposal is being submitted within the UK Research Centre in NDE (RCNDE) to the targeted research programme, the funding for which is earmarked by EPSRC for industrially driven research.

In an increasing number of industries, including those in the power generation, petrochemical and nuclear sectors, plant is extended beyond its original design life and there is a need to ascertain the integrity of areas that were not originally anticipated to require inspection. Guided acoustic waves provide the necessary range (tens of metres) for remote inspection and commercially available systems are routinely used for rapid screening of pipework. Recent research by the applicants has lead to the development of guided wave synthetic focusing techniques for pipe inspection, which have been shown to give an order of magnitude improvement in the sensitivity to small defects. However, the applicants have also shown that the quantitative information in the images is still not of sufficient resolution to enable sizing of critical defects to the accuracy required for structural integrity assessment. The reason why accurate sizing cannot be achieved is because, like other imaging systems, the resolvable detail is diffraction-limited by the wavelength of the probing wave. Resolution can be increased by operating at higher frequency but this is achieved at the expense of reduced range due to the increased attenuation and scattering. In many imaging fields so-called super-resolution techniques have been investigated that enable detail below the diffraction limit to be extracted. Although the benefits of super-resolution have been demonstrated in certain applications, its exploitation is highly case-specific. This is because, it must be tailored according to a priori knowledge of the interaction of the probing wave with the features likely to be encountered.The purpose of this project is to develop the use of sub-wavelength (super-resolution) characterisation techniques for the characterisation of otherwise inaccessible defects in safety-critical pipes using guided waves. The principal goal will be to determine the maximum penetration depth of a crack or corrosion patch, and also its orientation or shape. In discussion with the industrial collaborators the following target specifications have been agreed that represent the minimum that must be satisfied in order for guided wave sizing to be practically useful. The target will be to achieve a depth resolution of +/-0.1T (T = pipe wall thickness) for defects that are larger than 3T in lateral extent and deeper than 0.3T. This project will advance the understanding of guided wave scattering from realistic-shaped defects and will develop new super-resolution techniques to enable defects to be characterised using the scattered guided wave field collected by a transducer array. The project therefore involves basic science applied to a highly relevant industrial problem, which makes it appropriate for EPSRC funding.