In the last ten years there has been a surge of interest in non-modal analysis applied to standard problems in fundamental fluid mechanics. Even in simple flows, the behaviour predicted by these non-modal analyses can be completely different from - and far more accurate than - that predicted by conventional analyses, particularly for the types of flows found in industrial situations.The successful application of non-modal analysis to standard problems sets the scene for step changes in engineering practice. Nevertheless, some very significant challenges must be overcome. Firstly, the standard approach cannot handle the non-linear problems often found in engineering. Secondly, the standard approach is computationally expensive and cannot handle problems with many degrees of freedom. Thirdly, the standard approach deals with simple measures, such as kinetic energy density, while other measures are usually more pertinent for industrial situations. Encouragingly, applied mathematicians and engineers have made significant progress in all of these areas. This progress has revealed that a generalized formulation of the problem in terms of constrained optimization and variational methods, adapting and applying methods from the control and computational communities, will bridge the gap between standard flows and engineering problems.Our vision is that future generations of engineering Computational Fluid Dynamics (CFD) tools will contain modules that can perform non-modal analysis. If and when such analyses can be made practicable they are certain to change the way that engineers design fluid mechanical systems, such as combustion chambers, turbine blades, reaction chambers and ink jet printers. Furthermore, they can readily deal with transient effects and non-periodic time-varying base flows, which are often particularly relevant in engineering situations.This research will benefit UK industries that rely on the modelling and control of fluid mechanics and thermoacoustics. For example, the pharmaceutical industry will benefit from a better understanding of transition to turbulence and relaminarization in physiological flows, which is important for the application of drugs via the nose and upper airways; The gas turbine industry will benefit from being able to perform instant sensitivity analyses of their fuel injectors and to combine this with greater understanding of the thermo-acoustics that leads to combustion instability; and the wind turbine industry will benefit from an improved prediction of the sensitivity of an aerofoil to turbulence transition and results of exposure to a gust or to the wake of the preceding aerofoil.The investigators in this proposal are all founder members of the EPSRC-funded Advanced Instability Methods (AIM) Network, which was set up in January 2009 to explore the relevance of non-normal analysis to industrial problems. Through masterclasses and workshops in academia and industry and an increasing number of web-based resources, the network provides a route for dissemination and exploitation of this research.In summary, the objectives of this proposal are to bridge the gap between fundamental work and engineering practice, to embed these techniques in the engineering design cycle and to reinforce a growing centre of excellence within the UK in this area. The generalized framework proposed here, combined with two challenging engineering examples and the resources of the AIM Network, will make this possible and demonstrate it to a wider engineering community.

Potential Impact:
This research will benefit the commercial private sector in the UK, particularly industries that rely on modelling and control of fluid mechanics and thermoacoustics. For example: the pharmaceutical industry will benefit from a better understanding of transition to turbulence in physiological flows; the gas turbine industry will benefit from sensitivity analyses of their fuel injectors and from non-modal analysis of combustion instability; the industrial combustion, energy, chemical processing and pharmaceutical industries will benefit from improved capability to predict mixing rates and eventually pollutant formation; commercial CFD users will benefit from stability tools in post-processors and optimization routines; the inkjet printer industry will benefit from the potential to create non-spherical droplets; and the wind turbine industry will benefit from an improved understanding of the sensitivity of an aerofoil to turbulence transition. This research will increase the standard of technology and the global competitiveness of UK-based companies. It will accelerate investigation of new problems and provide new insight into current problems. This will lead to new industrial design tools that will help high tech UK industries to remain competitive in markets in which technological advantage plays a crucial commercial role. As university researchers, we can create a core technology with a wide range of applications, which would not normally be funded by a single company. This will provide benefits within three years through new insights into current problems. We have found that that our research has greatest impact when we interact with industrial code development teams as they adopt our research to the format that is most useful to them. This process will take three to ten years. In the long term, we anticipate that industry will invest over a ten to twenty year timescale, employing some of the original developers of the technique. In this project, researchers across four departments will have to tackle un-solved problems, interpret research from a variety of backgrounds and translate it into a format that can be easily understood by the industrial community. These activities will develop problem solving, communication and teamwork skills. The investigators are founder members of the EPSRC Advanced Instability Methods (AIM) Network. The core technology will be made available to all members - currently over 70 academic and 7 industrial. We have already developed tutorials, handouts and model numerical code that can be downloaded and adapted by members. We will augment this with industrial case studies, In the longer term, the core technology will be useful to other companies with similar questions. As part of the network, we are organizing workshops targeted at particular problems across a range of industries. We will approach other potential partners directly and use the Research Days at Imperial College and Masters projects students at Cambridge to start collaborations. The investigators have their own established links with industry. We have regular (usually quarterly) meetings with our industrial contacts and will use these as opportunities to showcase research, to explore new areas and to indentify potential impact. The individual investigators will take the lead for interaction with their own industrial contacts, bringing experience from the other investigators as required. The post doctoral researchers will be involved and, if appropriate, the PhD students will be placed within industry for a few months. There will be no IP related to the concept of the generalized framework itself because this is already freely available. IP may arise from the specific application of the concept. Any collaborative work with the above companies will be performed under existing agreements, such as those between Cambridge and Rolls-Royce and BP.