Résumé
A combustion instability in a combustor typical of aero-engines is analyzed and modeled thanks to a low order Helmholtz solver. A Dynamic Mode Decomposition (DMD) is first applied to the Large Eddy Simulation (LES) database. The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approx. 350 Hz) and it shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 650-700 Hz, it is postulated that the instability observed around 350 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated with the entropy spots being convected throughout the choked nozzle plays a key role. A Delayed Entropy Coupled Boundary Condition is then derived in order to account for this interaction in the framework of a 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 solver proves able to predict the presence of an unstable mode around 350 Hz, in agreement with both the LES and the experiments. This finding supports the idea that the instability observed in the combustor is indeed driven by the entropy/acoustic coupling.