ESTIMATION OF THE BREAKUP LENGTH FOR THE ANNULAR AND THE ROUND LIQUID JET USING LINEAR INSTABILITY ANALYSIS

A linear instability analysis of an inviscid annular liquid sheet emanating from an atomizer subjected to inner and outer swirling air streams and a non-swirl round liquid jet has been carried out. The dimensionless dispersion equation that governs the instability was derived and was 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 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. Also, the results for round liquid jet and planar liquid sheet show that the linear theory accurately predicts the variation in breakup length with jet velocity.