Editing Combustion (section)

==Instabilities==
Combustion instabilities are typically violent pressure oscillations in a combustion chamber. These pressure oscillations can be as high as 180{{nbsp}}dB, and long-term exposure to these cyclic pressure and thermal loads reduces the life of engine components. In rockets, such as the F1 used in the Saturn V program, instabilities led to massive damage to the combustion chamber and surrounding components. This problem was solved by re-designing the fuel injector. In liquid jet engines, the droplet size and distribution can be used to attenuate the instabilities. Combustion instabilities are a major concern in ground-based gas turbine engines because of {{NOx}} emissions. The tendency is to run lean, an equivalence ratio less than 1, to reduce the combustion temperature and thus reduce the {{NOx}} emissions; however, running the combustion lean makes it very susceptible to combustion instability.

The [[Thermoacoustic hot air engine|Rayleigh Criterion]] is the basis for analysis of thermoacoustic combustion instability and is evaluated using the Rayleigh Index over one cycle of instability<ref>John William Strutt, 3rd Baron Rayleigh, Sc.D., F.R.S.., Honorary Fellow of Trinity College, Cambridge; "The Theory of Sound", §322h, 1878:</ref>

<div style="text-align:center;"><math>G(x)=\frac{1}{T}\int_{T}q'(x,t)p'(x,t)dt</math></div>

where q' is the heat release rate perturbation and p' is the pressure fluctuation.<ref>A. A. Putnam and W. C. Dennis (1953) "Organ-pipe oscillations in a flame-filled tube", ''Fourth Symposium (International) on Combustion'', The Combustion Institute, pp. 566–574.</ref><ref>E. C. Fernandes and M. V. Heitor, [https://books.google.com/books?id=Je_hG6UfnogC&q=rayleigh+thermoacoustic+ "Unsteady flames and the Rayleigh criterion"] in F. Culick,  M. V. Heitor, and J. H. Whitelaw, ed.s, ''Unsteady Combustion'' (Dordrecht, the Netherlands:  Kluwer Academic Publishers, 1996), p. 4</ref>
When the heat release oscillations are in phase with the pressure oscillations, the Rayleigh Index is positive and the magnitude of the thermoacoustic instability is maximised. On the other hand, if the Rayleigh Index is negative, then thermoacoustic damping occurs. The Rayleigh Criterion implies that thermoacoustic instability can be optimally controlled by having heat release oscillations 180 degrees out of phase with pressure oscillations at the same frequency.<ref>Dowling, A. P. (2000a). "Vortices, sound and flame – a damaging combination". ''The Aeronautical Journal of the RaeS''</ref><ref>{{cite journal |doi=10.1080/00102202.2012.714020 |title=Temperature Response of an Acoustically Forced Turbulent Lean Premixed Flame: A Quantitative Experimental Determination |year=2013 |last1=Chrystie |first1=Robin S. M. |last2=Burns |first2=Iain S. |last3=Kaminski |first3=Clemens F. |journal=Combustion Science and Technology |volume=185 |pages=180–199|s2cid=46039754 }}</ref> This minimizes the Rayleigh Index.