Determination of the drop size during atomization of liquid jets in cross flow

TL;DR

This paper derives a cubic formula for drop size in liquid sprays in cross flows using conservation equations, validated by experimental data, and provides insights into drop size distribution based on gas velocity.

Contribution

It introduces a new analytical model for drop size in cross flow sprays, incorporating energy and mass balances, and relates drop size to flow parameters.

Findings

Model agrees well with experimental data

Provides a drop size-velocity cross-correlation

Enables estimation of drop size distributions

Abstract

We have used the integral form of the conservation equations, to find a cubic formula for the drop size in liquid sprays in cross flows. Similar to our work on axial liquid sprays, the energy balance dictates that the initial kinetic energy of the gas and injected liquid be distributed into the final surface tension energy, kinetic energy of the gas and droplets, and viscous dissipation incurred. Kinetic energy of the cross flow is added to the energy balance. Then, only the viscous dissipation term needs to be phenomenologically modelled. The mass and energy balance for the spray flows renders to an expression that relates the drop size to all of the relevant parameters, including the gas- and liquid-phase velocities. The results agree well with experimental data and correlations for the drop size. The solution also provides for drop size-velocity cross-correlation, leading to drop size distributions based on the gas-phase velocity distribution. These aspects can be used in estimating the drop size for practical applications, and also in computational simulations of liquid injection in cross flows.