Résumé
A combustion instability in a combustor terminated by a nozzle is analysed and mod- elled based on a low order Helmholtz solver. A Large Eddy Simulation (LES) of the corresponding turbulent, compressible and reacting flow is first performed and analysed based on Dynamic Mode Decomposition (DMD). The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approx. 320 Hz) and shows the presence of large entropy spots generated within the combustion chamber and con- vected down to the exit nozzle. The lowest purely acoustic mode being in the range 700 − 750 Hz, it is postulated that the instability observed around 320 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated with entropy spots being convected throughout the choked nozzle plays a key role. The DMD analysis allows to extract from the LES results a low-order model that confirms that the mech- anism of the low-frequency combustion instability indeed involves both acoustic and convected entropy waves. The Delayed Entropy Coupled Boundary Condition (Motheau et al. 2014) is implemented into a numerical Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz/DECBC solver pre- dicts the presence of an unstable mode around 320 Hz, in agreement with both LES and experiments.