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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.

The dynamic response of a classical (simplex style) swirl injector has been studied experimentally using a superscale transparent model with water as the working fluid. A unique mechanism was developed for imparting controlled perturbations to the injector inlet mass flow by successively blocking and opening tangential inlet flow passages using a rotating cap over the inlet ports. Two vortex chamber designs (long and short) were evaluated to assess the effect of this important design variable. High-speed imaging of the spray cone and air core/liquid interface inside the vortex chamber was used to assess dynamic behavior at frequencies up to 500 Hz. Resonant conditions were detected in both designs, and both measurements gave similar frequencies for the resonant peak. The resonant peak was compared against recent theory due to Ismailov and Heister ("Dynamic Response of Rocket Swirl Injectors, Part I: Wave results compare well only when the theory is adjusted to account for potential water hammer effects induced by the rotating cap. Nomenclature D n = diameter of nozzle, in. L v = effective vortex chamber length including 1 2 nozzle contraction length, in. L vc = vortex chamber length, in. P manifold = manifold pressure, psi P ullage = ullage pressure, psi R in = radius to centerline of inlet channel, in. R n = radius of nozzle, in. R t = radius of tangential inlet, in. R vc = radius of vortex chamber, in. r vc = radius of air core in vortex chamber, in. v t = velocity in tangential inlets = core disturbance amplitude (half-air-core diameter amplitude over mean diameter) avg = average total (included) spray angle, deg 0 = total spray angle fluctuation amplitude, deg

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