Symmetry breaking of azimuthal waves: Slow-flow dynamics on the Bloch sphere
Abel Faure-Beaulieu, Nicolas Noiray
Abstract
A low-order model is proposed to describe the slow-timescale dynamics of thermoacoustic limit cycles in an idealized annular combustion chamber. A quaternion ansatz for the acoustic pressure field enables a unified description of the impact of system asymmetries (nonuniform distribution of heat release rate or azimuthal mean flow), flame response delay, and stochastic forcing from turbulence upon the standing or spinning nature of the thermoacoustic modes.
Topics & Concepts
AnsatzPhysicsDynamics (music)Classical mechanicsLimit (mathematics)SpinningSymmetry (geometry)Field (mathematics)AzimuthForcing (mathematics)Symmetry breakingTurbulenceMechanicsNoise (video)CombustorQuaternionDistribution (mathematics)Rotation (mathematics)Quantum electrodynamicsPerpendicularCombustionVortexWork (physics)Dynamical system (definition)Standing waveVorticityThermoacousticsSpiral (railway)Stability (learning theory)InstabilityOscillation (cell signaling)Rotational symmetryCylinderCombustion and flame dynamicsNonlinear Dynamics and Pattern FormationAerodynamics and Acoustics in Jet Flows