Symmetry breaking modelling for azimuthal combustion dynamics

Annular combustors can exhibit azimuthal thermoacoustic instabilities, which can rotate as a spinning wave at the speed of sound in the azimuthal direction, oscillate as a standing wave with pressure nodes fixed in space, or be a linear combination of these. These oscillations happen if a positive feedback loop between acoustics and the response of the flames to the acoustics in the annulus occurs. This paper discusses how two different explicit symmetry breaking mechanisms affect the dynamics of these waves. We first show how small differences between the flame responses lead to one strong topological change in the dynamical system phase space, making the system prefer orientation angles at two azimuthal locations, one opposite of the other in the annulus, as found in the experiments. This symmetry breaking is modelled by directly perturbing the flame responses around the annulus with some scatter, to represent the effect of manufacturing tolerances of the burners. We then consider recent experimental evidence that the heat release rate of the flames depends on the spinning direction (clockwise or anticlockwise) when the system is spinning. In particular we model one experiment in which the flame response is found to be stronger when the wave rotates in the anticlockwise direction. We show that the statistics of the resulting model are qualitatively very similar to the experimental results showing a preference for spinning states in the anticlockwise direction