Instability of a swirling annular liquid sheet under the effect of gas flow oscillation

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This study investigates the linear instability of a swirling annular liquid sheet subjected to gas flow oscillation, a configuration representative of pressure swirl atomizers operating under unsteady combustion conditions. Utilizing the Floquet theory and a potential flow assumption, the parametric instability of the liquid sheet is analyzed to elucidate the coupling mechanisms between liquid sheet swirling and unsteady aerodynamics. The results demonstrate that the subharmonic mode consistently exhibits higher growth rates than the harmonic mode and may therefore play a dominant role in the primary atomization process. The instability response proves highly sensitive to forcing characteristics: low-frequency oscillations facilitate sheet breakup by merging discrete unstable regions into a continuous spectrum, while high-amplitude forcing induces multiple independent local maxima. Furthermore, geometrical and physical parameters, such as thinner liquid sheets and higher gas densities, significantly enhance the sheet susceptibility to aerodynamic modulation. A key finding of this work is the distinct mode sensitivity introduced by liquid swirl. In contrast to non-swirling flows, where gas flow oscillation typically induces isolated high wave number unstable regions, the presence of swirl facilitates direct modulation of the primary dispersion curve. Specifically, the coupling of centrifugal forces and unsteady aerodynamic forcing preferentially amplifies the axisymmetric and second non-axisymmetric (n=2) modes, while the helical mode (n=1) remains relatively unchanged. The presence of swirl significantly enhances the responsiveness of the annular liquid sheet to airflow oscillation, accelerating disintegration under oscillating flow conditions.

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