Deformation and drag properties of round drops subjected to shock-wave disturbances

The deformation, drag, and breakup properties of round drops subjected to shock-wave disturbances were studied computationally for conditions where effects of drop evaporation were small. The objective of the study was to consider effects of liquid viscosity, liquid/gas density ratio, and drop Reynolds number that are difficult to explore based on experiments but are representative of conditions found in practical sprays. The time-dependent incompressible and axisymmetric Navier-Stokes equations were solved in both the gas and liquid phases in conjunction with the level set method to determine the position of the liquid/gas interface for deforming drops. The numerical results were evaluated using earlier experimental results for the wake and drag properties of solid spheres and the deformation and drag and breakup properties of drops subjected to shock-wave disturbances. There was good agreement between measurements and predictions. The properties of drop deformation and breakup were mainly affected by the drop drag-force/surface-tension-force ratio represented by the Weber number We and the drop liquid-viscous-force/surface-tension-force ratio represented by the Ohnesorge number Oh. When the Oh was small, drop deformation and breakup transitions yielded the classical deformation and breakup regime map suggested by Hinze roughly 50 years ago. However, when the Oh was large the computations revealed undesirable variations of We as a function of Oh for particular deformation and breakup regime transitions when plotted in the classical Hinze form. An improved approach to handle large Oh conditions was found, however, by directly plotting the drop drag-force/liquid-viscous-force ratio We(1/2)/Oh, as a function of the drop surface-tension-force/liquid viscous-force ratio 1/Oh because We(1/2)/Oh is relatively independent of Oh at the regime transitions when the Oh is large. Effects of liquid/gas viscosity and density ratios on the new deformation and breakup regime map were found to be small. The Reynolds number of the gas flow over the drop, however, was found to have a considerable effect on drop deformation and breakup properties as the low Reynolds number (<100), Stokes flow, regime was approached. This behavior appears to be caused by the progressive increase of the drop drag coefficient when the Reynolds number of the gas flow becomes small, which tends to reduce drop relaxation times and thus times available for drop deformation and breakup.