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We have used the integral form of the conservation equations, to find a cubicformula for the drop size in liquid sprays in cross flows. Similar to our workon axial liquid sprays, the energy balance dictates that the initial kineticenergy of the gas and injected liquid be distributed into the final surfacetension energy, kinetic energy of the gas and droplets, and viscous dissipationincurred. Kinetic energy of the cross flow is added to the energy balance.Then, only the viscous dissipation term needs to be phenomenologicallymodelled. The mass and energy balance for the spray flows renders to anexpression that relates the drop size to all of the relevant parameters,including the gas- and liquid-phase velocities. The results agree well withexperimental data and correlations for the drop size. The solution alsoprovides for drop size-velocity cross-correlation, leading to drop sizedistributions based on the gas-phase velocity distribution. These aspects canbe used in estimating the drop size for practical applications, and also incomputational simulations of liquid injection in cross flows.

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