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Reference Number EP/J011126/1
Title Sum-of-Squares Approach to Global Stability and Control of Fluid Flows
Status Completed
Energy Categories ENERGY EFFICIENCY(Transport) 80%;
Research Types Basic and strategic applied research 100%
Science and Technology Fields ENGINEERING AND TECHNOLOGY (Mechanical, Aeronautical and Manufacturing Engineering) 100%
UKERC Cross Cutting Characterisation Not Cross-cutting 100%
Principal Investigator Professor SI Chernyshenko
No email address given
Imperial College London
Award Type Standard
Funding Source EPSRC
Start Date 23 February 2013
End Date 22 February 2016
Duration 36 months
Total Grant Value £336,962
Industrial Sectors Aerospace; Defence and Marine
Region London
Programme NC : Engineering
Investigators Principal Investigator Professor SI Chernyshenko , Aeronautics, Imperial College London (100.000%)
  Industrial Collaborator Project Contact , Airbus UK Ltd (0.000%)
Web Site
Abstract This project aims at developing new methods of analysis of the stability of fluid flows and flow control. Flow control is among the most promising routes for reducing drag, thus reducing carbon emissions, which is the strongest challenge for aviation today. However, the stability analysis of fluid flows poses significant mathematical and computational challenges. The project is based on a recent major breakthrough in mathematics related to positive-definiteness of polynomials. Positive-definiteness is important in stability and control theory because it is an essential property of a Lyapunov function, which is a powerful tool for establishing stability of a given system. For more than a century since their introduction in 1892 constructing Lyapunov functions was dependent on ingenuity and creativity of the researcher. In 2000 a systematic and numerically tractable way of constructing polynomials that are sums of squares and that satisfy a set of linear constraints was discovered. If a polynomial is a sum of squares of other polynomials then it is positive-definite. Thus, systematic, computer-aided construction of Lyapunov functions became possible for systems described by equations with polynomial non-linearity. In the last decade the Sum-of-Squares approach became widely used with significant impact in several research areas.The Navier-Stokes equations governing motion of incompressible fluid have a polynomial nonlinearity. This project will achieve its goals by applying sum-of-squares approach to stability and control of the fluid flows governed by these equations. This will require development of new advanced analytical techniques combined with extensive numerical calculations. The project has a fundamental nature, with main expected outcomes being applicable to a large variety of fluid flows. The rotating Taylor-Couette flow will be the first object to which the developed methods will be applied. Taylor-Couette flow, encountered in a wide range of industrial application, for a variety of reasons has an iconic status in the stability theory, traditionally serving as a test-bench for new methods.In order to maximise the impact of the research, the project collaborators will conduct targeted dissemination activities for industry and academia in the form of informal and formal workshops, in addition to traditional dissemination routes of journal papers and conferences. Selected representatives from industry will be invited to attend the workshops. Wider audience will be reached via a specially created and continuously maintained web page
Publications (none)
Final Report (none)
Added to Database 10/07/12