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Air-blast atomizers provide excellent atomization over a large range of fuel flow rates and very good penetration. In this study we consider an annular liquid sheet emanating from an air-blast atomizer subjected to inner and outer swirling air streams. A temporal stability analysis is carried out to model the atomization of a swirling viscous annular liquid sheet subject to axi-symmetric disturbances and inviscid swirling air streams. Numerical solutions to the dispersion equation under a wide range of flow conditions are carried out to investigate the effects of the liquid-gas swirling orientation on the maximum growth rate and its corresponding unstable wave number.