Uncertainty is ubiquitous in the mathematical characterisation of engineered and natural systems. In many structural engineering applications, a deterministic characterisation of the response may not be realistic because of uncertainty in the material constitutive laws, operating conditions, geometric variability, unmodelled behaviour, etc. Ignoring these sources of uncertainties or attempting to lump them into a factor of safety is no longer widely considered to be a rational approach, especially for high-performance and safety-critical applications. It is now increasingly acknowledged that modern computational methods must explicitly account for uncertainty and produce a certificate of response variability alongside nominal predictions. Advances in this area are key to bringing closer the promise of computational models as reliable surrogates of reality. This capability will potentially allow significant reductions in the engineering product development cycle due to decreased reliance on extensive experimental testing programs and enable the design of systems that perform robustly in the face of uncertainty. The proposed investigation will address this important research problem and deliver convergent computational methods and efficient software implementations that are orders of magnitude faster than direct Monte-Carlo simulation for predicting the response of structural systems in the presence of uncertainty. This work will draw upon developments in stochastic subspace projection theory which have recently emerged as a highly efficient and accurate alternative to existing techniques in computational stochastic mechanics. The overall objectives of this project include: (1) formulation of convergent stochastic projection schemes for predicting the static and (low and medium frequency) dynamic response statistics of large-scale stochastic structural systems. (2) design and implementation of a state-of-the-art parallel software framework that leverages existing deterministic finite element codes for stochastic analysis of complex structural systems, and (3) laboratory and computer experiments to validate the methods developed. The methods to be developed will find applications to a wide range of structural problems that require efficient and accurate predictions of performance and safety in the presence of uncertainty. This is a crucial first step towards rational design and control strategies that can meet stringent performance targets and simultaneously ensure system robustness. Progress in this area would also be of benefit to many other fields in engineering and the physical sciences where there is a pressing need to quantify uncertainty in predictive models based on partial differential equations.

A major design consideration for offshore wave energy devices is survivability under extreme wave loading. The aim of this project is to predict loading and response of two floating wave energy devices in extreme waves using CFD (computational fluid dynamics), in which fluid viscosity, wave breaking and the full non-linearity of Navier-Stokes and continuity equations are included. Two classes of device will be considered: Pelamis (of Ocean Power Delivery Ltd.), the prototype having already successfully generated electricity into the grid, and a floating buoy device responding in heave, known as the Manchester Bobber (Manchester University), which is being tested at 1/10th scale. Both classes of device are thought to be competitive with other renewable energy sources, being economically roughly equivalent to onshore wind energy. The CFD simulations will be undertaken in three ways: by commercial codes, CFX and COMET (STAR-CD); by recent advanced surface-capturing codes; and by the novel SPH (smoothed particle hydrodynamics) method. In order to address the uncertainties in the CFD approaches, such as the accuracy of prediction and the magnitude of computer resources required, a staged hierarchical approach of increasing computer demand will be taken in: mathematical formulation (from an inviscid single fluid to a two-fluid viscous/turbulence approach); wave description (from regular periodic to focussed wave groups including NewWave); and complexity of structure (from a fixed horizontal cylinder parallel to wave crests to the six degrees of freedom of Pelamis). At each stage, numerical results will be compared with experimental data. The significance of the inviscid v. viscous formulations, wave nonlinearity, non-breaking v. breaking conditions, and the dynamic response of the body will thus be assessed for extreme conditions. Designs for survivability should thus be better evaluated. The resulting CFD methodology will also benefit analysis of extreme wave interaction with ships, other marine vehicles and structures in general. For example interaction with freak waves and the 'green' water problem have yet to be resolved.

Fluid dynamics underpins large areas of engineering, environmental and scientific research, and is becoming increasingly important in medical science. At Leeds, we possess research expertise across each of these domains and we have an established record of working across disciplinary boundaries. This proposal builds upon this record through the establishment of a multidisciplinary CDT in Fluid Dynamics. Research techniques that will be applied, and developed, will encompass: mathematical modelling & theory; numerical methods, CFD & high performance computing (HPC); and measurement & experimentation. Engineering application areas to be addressed include: reacting flows; carbon capture, transport & storage; flow of polymer melts; mixing problems; particulate flows; coating & deposition; lubrication; medical devices; pathogen control; heat transport; wind turbines; fluid-structure interaction; and nuclear safety. Environmental application areas will consist of: groundwater flow; river/estuary flows; tidal flows; oceanography; atmospheric pollution; weather forecasting; climate modelling; dynamics of the Earth's interior; and solar & planetary flow problems. Facilities available to undertake this research include: the University's HPC system which, combined with the N8 regional facility that is hosted at Leeds, provides ~10000 computational cores, an extensive suite of licensed software and dedicated support staff; flow measurement techniques (including Particle Imaging Velocimetry (PIV), 2-component Laser Doppler Anemometry (LDA), Phase Doppler Anemometry (PDA) and Ultrasonic Doppler Velocity Profiling (UDVP)); techniques for measuring fluid concentration (Ultrasonic High Concentration Meter (UHCM) and Optical Backscatter Probes (OBS)) and a range of optical metrology systems (e.g. pulsed and continuous wave lasers). The UK has a substantial requirement for doctoral scientists and engineers who have a deep understanding of all aspects of fluid dynamics from theory through to experimental methods and numerical simulation. In manufacturing and process engineering, for example, many processes depend critically on fluid flows (e.g. extrusion of polymer melts, deposition of coatings, spray drying, etc.) and it is essential to understand and control these processes in order to optimize production efficiency and reliability (see letter of support from P&G for example). In large-scale mechanical engineering there is a demand for expertise in reacting turbulent flows in order to optimize fuel efficiency and engine performance, and in wetting and surface flows for the design and manufacture of pumps and filters. There is also a need for a wide variety of skilled experts in environmental fluid flows to support the growing need to understand and predict local pollution and threats to safety (atmospheric, surface water, ocean and sub-surface flows), and to predict weather, climate and space weather for satellite technology. We will train a new generation of researchers who will have a broad range of skills to transfer into industry and environmental agencies, hence our approach will be multi-disciplinary throughout. All students will undertake both modelling and experimental training before embarking on their PhD project - which will be co-supervised by academics from different Schools. The MSc component of the programmee will be specifically tailored to develop expertise in the mathematical background of fluid dynamics, in CFD/HPC, and in experimental techniques. Team-based projects will be used to develop the teamwork and communication skills we believe are essential. Finally, engagement with industry will be a key feature of this CDT: all students will undertake an industrial placement, a large number of projects will be industrially sponsored, and our non-academic partners will contribute actively to our management, implementation and strategic development.

The Transforming the Foundation Industries Challenge has set out the background of the six foundation industries; cement, ceramics, chemicals, glass, metals and paper, which produce 28 Mt pa (75% of all materials in our economy) with a value of £52Bn but also create 10% of UK CO2 emissions. These materials industries are the root of all supply chains providing fundamental products into the industrial sector, often in vertically-integrated fashion. They have a number of common factors: they are water, resource and energy-intensive, often needing high temperature processing; they share processes such as grinding, heating and cooling; they produce high-volume, often pernicious waste streams, including heat; and they have low profit margins, making them vulnerable to energy cost changes and to foreign competition. Our Vision is to build a proactive, multidisciplinary research and practice driven Research and Innovation Hub that optimises the flows of all resources within and between the FIs. The Hub will work with communities where the industries are located to assist the UK in achieving its Net Zero 2050 targets, and transform these industries into modern manufactories which are non-polluting, resource efficient and attractive places to be employed. TransFIRe is a consortium of 20 investigators from 12 institutions, 49 companies and 14 NGO and government organisations related to the sectors, with expertise across the FIs as well as energy mapping, life cycle and sustainability, industrial symbiosis, computer science, AI and digital manufacturing, management, social science and technology transfer. TransFIRe will initially focus on three major challenges: 1 Transferring best practice - applying "Gentani": Across the FIs there are many processes that are similar, e.g. comminution, granulation, drying, cooling, heat exchange, materials transportation and handling. Using the philosophy Gentani (minimum resource needed to carry out a process) this research would benchmark and identify best practices considering resource efficiencies (energy, water etc.) and environmental impacts (dust, emissions etc.) across sectors and share information horizontally. 2 Where there's muck there's brass - creating new materials and process opportunities. Key to the transformation of our Foundation Industries will be development of smart, new materials and processes that enable cheaper, lower-energy and lower-carbon products. Through supporting a combination of fundamental research and focused technology development, the Hub will directly address these needs. For example, all sectors have material waste streams that could be used as raw materials for other sectors in the industrial landscape with little or no further processing. There is great potential to add more value by "upcycling" waste by further processes to develop new materials and alternative by-products from innovative processing technologies with less environmental impact. This requires novel industrial symbioses and relationships, sustainable and circular business models and governance arrangements. 3 Working with communities - co-development of new business and social enterprises. Large volumes of warm air and water are produced across the sectors, providing opportunities for low grade energy capture. Collaboratively with communities around FIs, we will identify the potential for co-located initiatives (district heating, market gardening etc.). This research will highlight issues of equality, diversity and inclusiveness, investigating the potential from societal, environmental, technical, business and governance perspectives. Added value to the project comes from the £3.5 M in-kind support of materials and equipment and use of manufacturing sites for real-life testing as well as a number of linked and aligned PhDs/EngDs from HEIs and partners This in-kind support will offer even greater return on investment and strongly embed the findings and operationalise them within the sector.

With the present trend towards miniaturisation of devices and development of microscale processes, there has arisen the need for microscale heat transfer equipment. For instance, in microelectronic processors, heat transfer is becoming the limiting factor in relation to increasing performance. Convective heat transfer with phase change offers significant performance improvements over single phase cooling systems. However, in microscale channels the mechanisms controlling the phase change and flow distribution differ from those at the macroscale. This project comprises an experimental study to solve some of the problems associated with phase change in microchannels and also the numerical modelling of boiling/condensation theory to both aid in design of experiments and develop design procedures for heat exchange processes based on two phase flow in microchannels.Development of novel experimental techniques (eg microsensor for heat flux and temperature measurement, fluid diode) will enable characterisation of local parameters in both boiling and condensation and active control of the boiling process.State-of-the-art numerical techniques will supplement the experimental investigation, enabling results to be applied to other systems. This combination of experimentation using innovative microsensors and control systems, developed using advanced microfabrication facilities, with numerical modelling offers a unique opportunity for the development of design procedures for such microscale heat transfer systems.