Stability of high-frequency pressure oscillations in rocket combustion chambers

The problem of determining the stability of high-frequency pressure oscillations in rocket combustion chambers is treated explicitly as a perturbation of the classical acoustics problem. On the basis of previous experimental results, the energy addition hy combustion is emphasized, and an analysis is developed for tbe stability of stationary pressure waves in chammers using either liquid or gaseous propellants. The formulation is for the three-dimensional case; computations are carried out in detail for a cylindrical chamber in which the mean velocity is parallel to the axis and varies only with axial position. The principal result is a formula for the imaginary part of the complex frequency associated with each of the natural modes of the chamber. This yields a single dimensionless group as a measure of the stability of individual chamber modes. Because of the present lack of sufficiently detailed experimental evidence, quantitative interpretation seems impossible, but qualitative agreement with observations can be demonstrated