Spatio-temporal dynamics and disintegration of a fan liquid sheet

Abstract

The dynamic behavior and disintegration mechanisms of a fan liquid sheet in a quiescent atmosphere are investigated over a broad range of differential injection pressures up to Δ p ≈ 70 bar through experiments, proper orthogonal decomposition (POD) and spectral analyses, and linear stability analysis (LSA). By fan liquid sheet, we mean a diverging and attenuating liquid stream emanating from a flat fan nozzle with high velocity. High spatiotemporal resolution backlit images reveal the formation-growth-fragmentation process of bag-like structures along the fan liquid sheets, which we predict to be responsible for the overall breakup of the sheets through a mechanism known as "wavy corridor."Therefore, we propose a conjugate model based on LSA to take into account the role of different shear and surface tension-driven instabilities in defining the liquid sheet intact radius and primary droplet sizes. The predictions of LSA from the dynamic features of the liquid sheets, which mainly depend on the sheet Weber number W e, are consistent with the quantitative results obtained from the POD and spectral analyses of the images. While the Strouhal number S t and the intact radius R of the fan liquid sheets reduce like W e - 1 / 3 with increasing W e, the volume median diameter of primary droplets decreases like W e - 11 / 12. An image feature consolidation technique along with a machine-learning technique, receiver operating characteristic curve analysis, was used to estimate the mean diameter of spray droplets with a large range of sizes.