Matrix-free continuation of limit cycles and their bifurcations for a ducted premixed flame
Waugh, Iain C
Journal of Fluid Mechanics
Cambridge University Press
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Waugh, I. C., Kashinath, K., & Juniper, M. (2014). Matrix-free continuation of limit cycles and their bifurcations for a ducted premixed flame. Journal of Fluid Mechanics, 759 1-27. https://doi.org/10.1017/jfm.2014.549
Many experimental studies have demonstrated that ducted premixed flames exhibit stable limit cycles in some regions of parameter space. Recent experiments have also shown that these (period-1) limit cycles subsequently bifurcate to period-2n, quasiperiodic, multiperiodic or chaotic behaviour. These secondary bifurcations cannot be found computationally using most existing frequency domain methods, because these methods assume that the velocity and pressure signals are harmonic. In an earlier study we have shown that matrix-free continuation methods can e ciently calculate the limit cycles of large thermoacoustic systems. This paper demonstrates that these continuation methods can also e ciently calculate the bifurcations from the limit cycles. Furthermore, once these bifurcations are found, it is then possible to isolate the coupled ame-acoustic motion that causes the qualitative change in behaviour. This information is vital for techniques that use selective damping to move bifurcations to more favourable locations in the parameter space. The matrix-free methods are demonstrated on a model of a ducted axisymmetric premixed flame, using a kinematic G-equation solver. The methods nd limit cycles and period-2 limit cycles, and fold, period-doubling and Neimark-Sacker bifurcations as a function of the location of the flame in the duct, and the aspect ratio of the steady flame.
Iain Waugh acknowledges the support of EPSRC through a Doctoral Training Grant and the IMechE through the postgraduate scholarship award. Karthik Kashinath acknowledges the support of EPSRC and Rolls-Royce through a Dorothy Hodgkin studentship. Matthew Juniper acknowledges the support of the ERC through project ALORS 2590620.
External DOI: https://doi.org/10.1017/jfm.2014.549
This record's URL: https://www.repository.cam.ac.uk/handle/1810/246177
Attribution-NonCommercial 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by-nc/2.0/uk/
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