Breakup of a liquid drop suddenly exposed to a high-speed airstream

The breakup of viscous and viscoelastic drops in the high speed airstream behind a shock wave in a shock tube was photographed with a rotating drum camera giving one photograph every 5μs. From these photographs we created movies of the fragmentation history of viscous drops of widely varying viscosity, and viscoelastic drops, at very high Weber and Reynolds numbers. Drops of the order of one millimeter are reduced to droplet clouds and possibly to vapor in times less than 500 μs. The movies may be viewed at http://www.aem.umn.edu /research/Aerodynamic_Breakup. They reveal sequences of breakup events which were previously unavailable for study. Bag and bag-and-stamen breakup can be seen at very high Weber numbers, in the regime of breakup previously called “catastrophic.” The movies allow us to generate precise displacement-time graphs from which accurate values of acceleration (of orders 10 to 10 times the acceleration of gravity) are computed. These large accelerations from gas to liquid put the flattened drops at high risk to Rayleigh-Taylor instabilities. The most BREAKUP OF A LIQUID DROP SUDDENLY EXPOSED TO A HIGH-SPEED AIRSTREAM 2 unstable Rayleigh-Taylor wave fits nearly perfectly with waves measured on enhanced images of drops from the movies, but the effects of viscosity cannot be neglected. Other features of drop breakup under extreme conditions, not treated here, are available on our Web site. 1. Fragmentation of Newtonian and viscoelastic drops The problem of aerodynamic breakup of liquid drops has given rise to a large literature. Most of the early literature focuses on drops of Newtonian liquids in subsonic air streams, and is excellently reviewed by Pilch & Erdman (1987), and Hsiang and Faeth (1992). Shock tube studies of the breakup of Newtonian drops, usually water, under high subsonic and supersonic conditions were carried out by Hanson and Domich (1956), Engel (1958), Hanson, Domich, & Adams (1963), Ranger and Nicholls (1969), Reinecke & McKay (1969), Reinecke & Waldman (1970, 1975), Waldman, Reinecke & Glenn (1972), Simpkins & Bales (1972), Wierzba and Takayama (1988), Yoshida & Takayama (1990), Hirahara and Kawahashi (1992), and others. The excellent study of Engel (1958) showed that water drops of millimeter diameter would be reduced to mist by the flow behind an incident shock moving at Mach numbers in the range 1.3 to 1.7. Many of the other aforementioned studies allude to the presence of large amounts of mist. Joseph, Huang and Candler (1996) argued that mist could arise from condensed vapor under flash vaporization due to (1) low pressures at the leeside produced by rarefaction and drop acceleration, (2) high tensions produced by extensional motions in the liquid stripped from the drop, (3) the frictional heating by rapid rates of deformation, and (4) the heating of sheets and filaments torn from the drop by hot air. Though mist and vapor formation is not the focus of this study, it is relevant that the Rayleigh-Taylor instability pumps fingers of hot gas behind the shock into the drop increasing both the frictional heating and the area of liquid surface exposed to hot gas. The recent and fairly extensive literature on atomization is well represented in the papers by Hsiang and Faeth (1992), Hwang, Liu and Rietz (1996), and Faeth (1996). These results, and earlier drop breakup studies such as Krzeczkowski (1980), Wierzba (1990), Kitscha and Kocamustafaogullari (1989), and Stone (1994), are restricted to relatively low Weber and Reynolds numbers. The highest Weber and Reynolds data for drop breakup was reported by Hsiang and Faeth (1992) who worked under conditions for which the Weber numbers ranged from 0.5 to 1000 with Reynolds numbers from 300-1600. High Weber number drop breakup data were obtained by Engel (1958), Ranger and Nichols (1969), and Reinecke and Waldman (1970) for air and water only, so viscous effects could not be BREAKUP OF A LIQUID DROP SUDDENLY EXPOSED TO A HIGH-SPEED AIRSTREAM 3 studied. In contrast, the data presented here cover a wide range of viscosities (from 0.001 to 35 kg/m sec) and a wide range of high Weber numbers (from 11700 to 169000), Ohnesorge numbers (from 0.002 to 82.3) and Reynolds numbers (from 40000 to 127600), based on the freestream conditions. Another feature which distinguishes our experiments from previous ones is that we have recorded all of the data as real time movies which may be seen under “video animations” at our Web address. The movies capture events which were previously unknown, such as bag breakup and bag-and-stamen breakup of high viscosity drops at very high Weber numbers, whereas short wave Rayleigh-Taylor corrugations appear on water drops under similar free stream conditions (see figure 19). The thesis of this paper is that breakup at high accelerations, corresponding to high Weber numbers, is controlled at early times by Rayleigh-Taylor instabilities. We back up this claim by comparing theory with experiment. From the movies we get accurate displacement-time graphs, one point ever 5 μs, from which the huge accelerations which drive Rayleigh-Taylor instabilities can be measured. The movie frames can be processed for images of unstable waves from which the length of the most dangerous wave can be measured and compared with theory. Only a few studies of the breakup of viscoelastic drops have been published; Lane (1951), Wilcox, June, Braun and Kelly (1961), Matta and Tytus (1982), and Matta, Tytus and Harris (1983). Matta and co-workers did studies at Mach numbers near one and less. They showed that threads and ligaments of liquid arise immediately after breakup, rather than the droplets which are seen in Newtonian liquids. We have verified these general observations for more and different liquids in high speed air behind shocks with Mach numbers as high as 3. These structures can be seen in the photographs in figures 1-13 of this paper which show just a few frames from the respective movies on our web page. For example, compare figure 1, which shows the breakup of a water drop in our shock tube at a shock Mach number of 2, with figures 5 and 7 which show respectively the breakup under the same conditions of a 2% aqueous solution of polyox and a 2.6% solution of polystyrene butylacrylate in tributyl phosphate. Figures 2, 6, and 8 show the breakup of the same liquids at a shock Mach number of 3. BREAKUP OF A LIQUID DROP SUDDENLY EXPOSED TO A HIGH-SPEED AIRSTREAM