The subject of main engine combustor stability is viewed from the perspective of two interacting dynamic chambers — on the one hand, the premixing or vaporizing chamber which supplies fuel ladened air to a second chamber where combustion takes place. The system is modeled with each of the two chambers as a Helmholz resonator each with an orifice to a constant reference pressure, and with a third orifice interconnecting the two subsystems. Futhermore, it is hypothesized that a dynamic heat release is possible which is proportional to the velocity of the fuel ladened air exiting from the premixing chamber into the combustion chamber. On the basis of this model, a stability criterion is derived which gives the critical combustor temperature ratio as a function of geometry of the combustor — the two-chamber volumes and the effective perimeters and areas of the orifices. Additionally, the frequency of oscillation of the unstable system is derived as a function of these same parameters. The analytic result suggests that the most potent configuration detail that can be manipulated to eliminate or avoid instability is ratio of the natural frequency of the premixing chamber of the natural frequency of the combustion chamber (as computed with the passage between the premixing chamber and the combustion chamber blocked). If this ratio can be maintained above unity, stability is assured.

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