Combustion instability
For instance, thermoacoustic instabilities are a major hazard to gas turbines and rocket engines.
For example, the numerous tests required to develop rocket engines [4] are largely in part due to the need to eliminate or reduce the impact of thermoacoustic combustion instabilities.
Their associated pressure oscillations can have well defined frequencies with amplitudes high enough to pose a serious hazard to combustion systems.
This feedback between the acoustic waves in the combustor and the heat-release fluctuations from the flame is a hallmark of thermoacoustic combustion instabilities.
The conditions under which perturbations will grow are given by Rayleigh's (John William Strutt, 3rd Baron Rayleigh) criterion:[10] Thermoacoustic combustion instabilities will occur if the volume integral of the correlation of pressure and heat-release fluctuations over the whole tube is larger than zero (see also thermoacoustics).
Combining the above two conditions, and for simplicity assuming here small fluctuations and an inviscid flow, leads to the extended Rayleigh's criterion.
Likewise, a stronger driving of a combustion instability happens when the heat is released at a higher pressure.
To picture heat-release fluctuations due to mixture inhomogeneities, consider a pulsating stream of gaseous fuel upstream of a flame-holder.
Such a pulsating stream may well be produced by acoustic oscillations in the combustion chamber that are coupled with the fuel-feed system.
Heat-release fluctuations produced by hydrodynamic instabilities happen, for example, in bluff-body-stabilized combustors when vortices interact with the flame (see previous figure).
[12] Lastly, heat-release fluctuations due to static instabilities are related to the mechanisms explained in the next section.
[13] To explain these phenomena, consider a flame that is stabilized with swirl, as in a gas-turbine combustor, or with a bluff body.
For a fixed fuel-oxidizer ratio, increasing the oncoming velocity makes the flame behave in a similar way to the one just described.
Even though the processes just described are studied with experiments or with Computational Fluid Dynamics, it is instructive to explain them with a simpler analysis.
In this analysis, the interaction of the flame with the flow environment is modeled as a perfectly-mixed chemical reactor.
This is how this simple model captures qualitatively the more complex behavior explained in the above example of a swirl or bluff-body-stabilized flame.
