We have used the integral form of the conservation equations, to find a cubic formula for the drop size during in liquid sprays in coflow of air (air-blast atomization). Similar to our previous work, the energy balance dictates that the initial kinetic energy of the gas and injected liquid will be distributed into the final surface tension energy, kinetic energy of the gas and droplets, and viscous dissipation. Using this approach, the drop size can be determined based on the basic injection and fluid parameters for “air-blast” atomization, where the injected liquid is atomized by high-speed coflow of air. The viscous dissipation term is estimated using appropriate velocity and length scales of liquid–air coflow breakup. The mass and energy balances 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 velocities and fluid properties. 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 computed drop size distributions based on the gas-phase velocity distribution. This approach can be used in the estimation of the drop size for practical sprays and also as a primary atomization module in computational simulations of air-blast atomization over a wide range of injection and fluid conditions, the only caveat being that a parameter to account for the viscous dissipation needs to be calibrated with a minimal set of observational data.

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