Combustion Instabilities and Rayleigh's Criterion

In 1878, Lord Rayleigh formulated his criterion to explain several examples of acoustic waves excited and maintained by heat addition. It is a qualitative explanation successfully capturing the essence of the phenomena but not providing a basis for quantitative predictions. The widespread appeal of Rayleigh's criterion merits placing this important result on a more rigorous basis. To do so requires careful formulation grounded in the theory of small amplitude motions in a compressible fluid. In this chapter, we review the construction of an approximate analysis and establish the equivalence of Rayleigh's criterion and the condition for linear stability of small amplitude motions. Thus Rayleigh's criterion is formulated explicitly in the context of an analysis applicable to any combustion chamber. Some results are discussed for both linear and nonlinear motions. Recent experimental results discussed by others suggest that the criterion may offer a practical means for investigating the causes of instabilities in propulsion systems.