Cubic formula for determination of the drop size during atomization of liquid jets in co- and cross-flow of air

Using the integral formulation of the conservation equations as in our previous work, we can determine the drop size and its distributions in liquid sprays in co- and cross flow of air. 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. The mass and energy balance for the spray flows render to an expression that relates the drop size to all of the relevant parameters, including the gas- and liquid-phase properties and 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 distributions. These aspects can be used in estimating the drop size for practical applications, in synthesizing the data as a function of relevant variables, and also in integration into CFD for atomization algorithm.