Dynamic Response of Rocket Swirl Injectors, Part I: Wave Reflection and Resonance

Linear analyses are developed to theoretically investigate how disturbance waves are reflected and transmitted in the vortex chamber of a classical swirl injector. The dependence of the magnitude of the wave reflection process on the disturbance frequency is derived, and it is shown that this dependence may exhibit distinct maximum values. It is explained that the frequencies at which maximum response occurs are termed the resonant frequencies of the swirl injector. In general, resonant conditions will depend not only on the geometry of the injector but also on the particular flow conditions. In other words, for a given injector geometry, there are specific flow conditions that may produce resonance. A simple formula is derived for the primary resonance, which corresponds to a quarter-wave oscillation within the vortex chamber. Two different resonance theories are presented that vary in their level of accuracy of description of the flow transition from the vortex chamber to the nozzle. Results are provided for both of these models.