Some combustors enter a high-amplitude, almost single-frequency oscillation at particular operating points. The noise is unpleasant; the real problem is that the pressure amplitude multiplies the structural and thermal loads.
The mechanism
The oscillation arises from a feedback loop between heat release and the acoustic pressure wave. If the fluctuation in heat release is in phase with the pressure wave, combustion pumps energy into the acoustic wave; the wave in turn modulates the mixing and flow velocity and makes the heat release fluctuate again. The loop closes and the amplitude grows until non-linear effects limit it.
What decides it is the phase relationship: in phase it feeds, out of phase it damps.
Why it is hard to design out
The phase relationship depends on the time for fuel to travel from the injection point to the flame zone (the convective delay) and on the acoustic length of the chamber. Both change with the operating point. A system stable at one load can therefore be unstable at another, and the instability typically appears in the field, over a narrow operating band.
It is no coincidence that low-NOx designs are more prone to this: lean, premixed combustion makes the heat release more sensitive to flow fluctuations. See the NOx note.
The modelling approach
A full solution is expensive: the acoustic waves and the heat release fluctuation have to be solved together, meaning a compressible and transient computation. Because the Mach number is low, it is also numerically demanding.
The practical route has two steps: extract the acoustic modes of the chamber separately, then determine how the flame responds to those modes (the flame transfer function). Combining the two gives the stability map.
Passive remedies
Helmholtz resonators, acoustic liners, changing the fuel supply impedance. All are tuned to a particular frequency, and the job of the analysis is to predict that frequency and amplitude in advance.
References
- Magnussen, B. F. & Hjertager, B. H. (1977). On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. Symposium (International) on Combustion, 16(1), 719–729. DOI: 10.1016/S0082-0784(77)80366-4
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6