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

Abstract- 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. The instability and breakup of a liquid sheet is encountered in the liquid atomization process used in numerous applications including liquid fuel injection in combustion engines, spray drying of foods and detergents, and in manufacturing of pharmaceutical products [2], The growth of disturbances on the jet liquid-air interface leads to sheet instability and breakup, and governs the characteristics of the resulting spray. These characteristics play an important role in determining the subsequent heat/mass transport and phase change processes. For example, the liquid sheet instability and breakup in the fuel atomizer in combustion engines determines the mean drop size in the fuel spray and has direct impact on combustion efficiency, pollutant emissions and combustion instability. Due to good atomization characteristics and low liquid pressure requirements, air-blast atomizers are being considered in many applications. In an air- blast atomizer, the kinetic energy of the high-speed swirling airstreams is used to breakup the liquid sheet. The liquid exits the air-blast atomizer as an annular sheet and is subjected to swirling inner and outer air streams [3], The presence of the atomizing air leads to shorter breakup length and enhances liquid air mixing [4, 5], A linear instability analysis of an inviscid swirl annular li