The Effects of Shock Strength on Droplet Breakup

The breakup of droplets occurs in the combustion of multiphase mixtures and the atomization of liquid jets. Most experiments studying droplet breakup have used the passage of a normal shock to provide a step change to uniform flow conditions. In the late 1950s, Engel [2] investigated how water droplets of various sizes broke up in the flow behind air shocks of different strengths. The subsequent deformation and breakup of the water droplets were captured using spark pictures, and a fine mist was observed to develop in the wake of the disintegrating droplet. Using drift measurements, an attempt was made to calculate the accelerations and unsteady drag coefficients of the deforming water droplets. Engel’s analysis concluded that the drag coefficient compared well to that for a perforated disk. In his recent review, Theofanous [10] summarized the aerobreakup of both Newtonian and viscoelastic liquid drops, and highlighted the criticalities in the breakup process. Also discussed were the interactions between the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, and the interplay of the multitude of length and time scales present in the problem. Using the novel diagnostic of laser-induced fluorescence, the experiments of Theofanous et al. [11] were able to achieve the necessary temporal and spatial resolutions to identify two primary breakup regimes: Rayleigh-Taylor piercing and shear-induced entrainment. Unfortunately, three-dimensional (3D) simulations are often too computationally expensive to allow direct comparisons with droplet experiments. Therefore, breakup is often studied using two-dimensional (2D) simulations which are physically equivalent to the breakup of liquid columns or cylinders. The work of Igra and Takayama [4, 5] provides useful validation for 2D simulations since their experiments investigated the breakup of water cylinders in the flow behind a shock wave. Columns with initial diameters of 4.8 and 6.4mm were impacted by Mach 1.18, 1.30, 1.47,