The Rayleigh criterion is an important stability criterion for self-excited combustion oscillations.

To enable a resonance frequency to be excited in a combustion chamber, a noise source is required which provides energy at the correct oscillation frequency and energy to this system continuously. In a combustion system, energy is supplied through oscillation of the reaction rate or the thermal combustion power rating at its mean value. However, in order for this thermal power oscillation to excite a self-excited combustion oscillation, it needs not only to have the correct frequency but also requires the correct phase angle, which amplifies the pressure oscillation that develops in the system. Lord Rayleigh was the first person to formulate this criterion back in 1878, and it therefore bears his name. It states that when the heat-release of the flame and pressure oscillation share the same phase, combustion oscillation is excited and, when these phases are opposed, that oscillation is damped. This consideration was picked up by Putnam and Dennis and was expressed mathematically in the form of the "Rayleigh Integralx94:

This integral states that the product of thermal power oscillation and sound pressure must be positive when integrated over an oscillation period TP to enable combustion oscillation to be excited. If the integral value is negative, the combustion oscillation is damped.

If this same equation is applied to a harmonic oscillation, the condition is satisfied if the phase difference between thermal power oscillation and sound pressure oscillation in the range ± 90°.

Consistent further development of this criterion has yielded the investigations by ourselves of the 1 and 2-dimensional Rayleigh index. To this end, the global formulation of the above non-balancing equation was extended into a local formulation in the form of an index. This index enables the exciting and damping ranges within a combustion zone to be identified which in turn means that the link between thermal and acoustic oscillation can be influenced.

This figure illustrates the 1 and 2-dimensional Rayleigh index, calculated on the basis of experimental data of a combustion chamber for liquid aviation fuel. The one-dimensional Rayleigh index is depicted as a curve over the length of the burner (lower Fig.) and the 2-dimensional Rayleigh index is shown as an intensity figure in the burner geometry (upper Fig.). It can be seen here that the excited and damped flame areas alternate along the combustion chamber, with excited areas being more dominant. This in turn causes the excitation of combustion oscillations.