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Matrix-free continuation of limit cycles and their bifurcations for a ducted premixed flame

Waugh, IC and Kashinath, K and Juniper, MP (2014) Matrix-free continuation of limit cycles and their bifurcations for a ducted premixed flame. Journal of Fluid Mechanics, 759. pp. 1-27. ISSN 0022-1120

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© Cambridge University Press 2014. 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 efficiently calculate the limit cycles of large thermoacoustic systems. This paper demonstrates that these continuation methods can also efficiently calculate the bifurcations from the limit cycles. Furthermore, once these bifurcations are found, it is then possible to isolate the coupled flame-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 find 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.

Item Type: Article
Divisions: Div A > Energy
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:37
Last Modified: 30 Jul 2020 15:04
DOI: 10.1017/jfm.2014.549