Unified limit-cycle amplitude prediction and symmetry-breaking analysis of combustion instabilities

• DOI: 10.1017/jfm.2025.10
• Publication Date: 2025-03-17T04:53:27Z
• Authors: V. Latour; D. Durox; A. Renaud; S. Candel
• Keywords: Limit cycle

Combustion instability analysis in annular systems often relies on reduced-order models that represent the complexity of combustion dynamics a framework which flame is represented by ‘flame describing function’ (FDF), portraying its heat release rate response to acoustic disturbances. However, most cases, FDFs are only available for limited range disturbance amplitudes, complicating description saturation process at high oscillation levels leading establishment limit cycle. This article shows this difficulty may be overcome using novel experimental scheme, relying injector staging and amplitude cycle can controlled, enabling us measure from simultaneous pressure recordings. These data then exploited replace standard modelling, expressed as third-order polynomial fluctuations, function modulation amplitude, allowing an easier adaptation data. The FDF used dynamical analyse set configurations combustor, where two families injectors mixed form different patterns. limit-cycle amplitudes coupling modes observed experimentally suitably retrieved. Finally, expression growth derived slow-flow variable equations defining modal phase functions, shown exactly agree with obtained previously energy principles, providing theoretical link between rates amplitudes.