Effect of confinement on weakly nonlinear temporal instability analysis of a viscous planar liquid sheet sandwiched between two co-flowing gas streams at equal velocities

Abstract

Extensive number of applications like rocket jet engine and gas turbines carry out atomization within a confined environment as it provides faster atomization and good mixing efficiency. Literature suggests that the effect of confinement on breakup of droplets, liquid threads, and annular jets is not elementary, but it varies with liquid viscosity, surrounding medium viscosity, and the confinement strength. Through the present weakly nonlinear temporal analysis, we unveil if a similar dynamic effect of confinement persists on the breakup of planar two-dimensional liquid sheets of varying viscosities. Moreover, to mimic air assisted atomization, the surrounding gases are considered to be flowing with non-zero velocities. Our study reveals that presence of confinement at higher gas-to-liquid velocity ratios of 2.5 and 3 produces no apparent improvement in atomization at all liquid Reynolds numbers. However, at relatively low gas-to-liquid velocity ratios of 2 and 2.25, confinement produces faster breakup as compared to an unconfined one, more so when Reynolds number is relatively low (Re < 100). The overall influence of confinement on non-dimensional breakup time is, however, weak as compared to how it affects the linear growth rate. A counteracting effect of confinement on the linear maximum growth rate and normalized second order disturbance amplitude is identified as the primary reason. Our study also identifies the minimum confinement height CH-1 which is just enough for the liquid sheet to achieve breakup without touching the solid walls. Interestingly, the maximum linear growth rate and minimum breakup time for a particular flow condition are always registered when confinement height equals to CH-1. The values of CH-1 display a strong dependence upon Reynolds number and gas-to-liquid velocity ratios.