A linear instability analysis of an inviscid annular liquid sheet emanating from an atomizer subjected to inner and outer swirling air streams has been carried out. The dimensionless dispersion equation that governs the instability is derived. The dispersion equation solved by Numerical method to investigate the effects of the liquid-gas swirl orientation on the maximum growth rate and its corresponding unstable wave number that it produces the finest droplets. To understand the effect of air swirl orientation with respect to liquid swirl direction, four possible combinations with both swirling air streams with respect to the liquid swirl direction have been considered. Results show that at low liquid swirl Weber number a combination of co-inner air stream and counter-outer air stream has the largest most unstable wave number and shortest breakup length. The combination of inner and the outer air stream co-rotating with the liquid has the highest growth rate.

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