AIM (Advanced Instability Methods) for industry

Lead Research Organisation: Imperial College London
Department Name: Dept of Aeronautics


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.


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Cantwell C (2015) Nektar++: An open-source spectral/ h p element framework in Computer Physics Communications

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Foures D (2013) Localization of flow structures using -norm optimization in Journal of Fluid Mechanics

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Foures DP (2012) Variational framework for flow optimization using seminorm constraints. in Physical review. E, Statistical, nonlinear, and soft matter physics

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Illingworth S (2013) Finding thermoacoustic limit cycles for a ducted Burke-Schumann flame in Proceedings of the Combustion Institute

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Illingworth, S (2014) Acoustic state space models using a wave-based approach in 21st International Conference on Sound and Vibration

Description We have transferred developments in non-modal stability analysis from the applied maths community to the engineering community. These techniques span a large class of engineering problems. In combustion instability, one of the application areas of the research, we have checked the results experimentally and see how to embed the process within the design cycle. This will be done in future research projects. One objective of the grant was to enable the UK to become the centre for the engineering application of non-modal stability analysis. There were many publications and conference presentations that arose from this project, as intended. Even better for this objective, one of the main architects of the application of this analysis to fluid mechanics, who was a partner on the proposal, moved from overseas to the UK during the grant. Regarding the technical objectives, we successfully developed and tested the generalized framework for non-modal stability analysis and applied it to the two situations envisaged. We have developed stability analysis methods for complex geometry flows which are now available in an open access software package, Nektar++. Not only have we provided methods to analyse two dimensional (biglobal) geometries using classical eigenvalue analysis as well as singular value decomposition we have also extended these techniques to so called Triglobal problems where one can analyse the instability pas a three-dimensional flow. Using triglobal analysis we have investigated how spanwise blowing and sucking can suppress vortex shedding of flow past a circular cylinder. Whilst the analysis is at low Reynolds numbers the instability persist to higher Reynolds numbers and so has potential broader application. We have developed a mathematically rigorous method to determine the best way to mix fluids with different properties with a fixed amount of energy input. This method can be applied to a wide range of engineering problems, in a range of flow geometries. Now that we have developed the DAL method for mixing problems, it can be applied to a wide range of situations. Possible future directions include optimising mixing in fluids with non-newtonian rheologies, flows in complicated geometries, or reacting flows, where the mixing also has a dynamical effect.
Exploitation Route We continue to get request about the usage of the stability tools within this package. It has also been used as part of an European training network where we have extended the technique to fully 3D (Triglobal) methods. The package continues to be used in related grant within our own group. There are now publication in the leading Journal of Fluid Mechanics using our tools by groups in Poland (Stan Gepner) and Australiia (Liang Cheng)
Sectors Aerospace, Defence and Marine,Healthcare

Description Council of Science and Technology Review on Modelling
Geographic Reach National 
Policy Influence Type Membership of a guideline committee
Description EC: IDIHOM
Amount £196,452 (GBP)
Funding ID 265780 
Organisation European Commission 
Sector Public
Country European Union (EU)
Start 07/2010 
End 06/2013
Description EU European Training Network:SSeMID
Amount £220,000 (GBP)
Funding ID 675008 
Organisation European Commission 
Sector Public
Country European Union (EU)
Start 01/2016 
End 01/2020
Description EU Research Training Network: ANADE
Amount £440,515 (GBP)
Funding ID 289428 
Organisation European Commission 
Sector Public
Country European Union (EU)
Start 12/2012 
End 11/2016
Description McLaren Group PhD funding
Amount £174,400 (GBP)
Organisation McLaren Group 
Sector Private
Country United Kingdom
Start 12/2007 
End 11/2011
Description RAEng/McLaren Research Chair
Amount £200,000 (GBP)
Organisation Royal Academy of Engineering 
Sector Learned Society
Country United Kingdom
Start 10/2012 
End 09/2017
Description McLaren Racing 
Organisation McLaren Racing
Country United Kingdom 
Sector Private 
PI Contribution We have transferred fundamental ideas behind vortex stability and identification to their design practice. More recently we are been applying computational modelling tools developed in an academic setting to example flow problems of direct interest to McLaren.
Collaborator Contribution Data and motivation on how to focus our research direction
Impact .
Start Year 2007
Title Nektar++ version 4.0.1 
Description Nektar++ is a tensor product based finite element package designed to allow one to construct efficient classical low polynomial order h-type solvers (where h is the size of the finite element) as well as higher p-order piecewise polynomial order solvers. 
Type Of Technology Software 
Year Produced 2014 
Open Source License? Yes  
Impact The software is being used by a number of national and international groups and our web site is currently being visited up to 100 times a day according to google analytics