Weakly nonlinear instability analysis of viscous planar liquid sheet under varicose mode of initial disturbance with co-flowing gas streams and prediction of resulting spray characteristics

Abstract

A theoretical investigation of the effects of viscosity is presented for breakup of a planar viscous liquid sheet subjected to a fundamental varicose mode of disturbance in the presence of moving gas medium. A classic perturbation technique up to second order has been employed to derive the linear and nonlinear interface disturbances. The breakup model is coupled with Maximum Entropy Formalism to predict the final spray characteristics. Findings reveal that within an initial range of Re, imposition of first harmonic on the fundamental disturbance produces a faster breakup as compared to the fundamental disturbance alone. As a result, first harmonic produces a destabilizing effect in the first regime, whose range is identified as 1 <Re < 20.3, 1<Re < 13.35 and 1<Re < 10.53 for gas velocity ratio 2.25, 2.50 and 2.75, respectively. Above this initial range of Re, first harmonic exhibits a stabilizing effect as it produces a delayed breakup when compared with the fundamental mode alone. However, a larger increase in dominating linear growth rate with Re negates the reduction of first harmonic in the destabilizing regime as well its damping effect in the stabilizing regime, resulting in an overall reduction in breakup time with the increase in Reynolds number. Analysis of spray characteristic suggests formation of finer droplets at higher gas velocity ratios. Moreover, reduction in liquid viscosity decreases the range of droplet diameter for gas velocity ratios 2.25 and 2.50.