Interactions Between Shock Waves and Liquid Droplet Clusters: Interfacial Physics

Abstract

Abstract This study quantitatively investigates the behaviors of single and multiple liquid cylinders placed in the path of a traveling normal shock wave using high-fidelity numerical simulations. The research is motivated by next-generation liquid-fueled scramjet and rotating detonation engines (RDE) where the liquid fuel interacts with shock waves and undergoes deformation, fragmentation, atomization, and vaporization before it mixes with the air and subsequently burns—the focus of this study is on the deformation and interfacial physics. The mathematical formulation to investigate this multiphase problem is based on a modified five-equation Kapila model that incorporates pressure-relaxation, viscous, and surface tension effects. A diffuse interface method is used to capture the liquid–gas interface. Two configurations are studied in this effort: (1) a single column of diameter 22 mm exposed to a shock wave traveling at Mach 2.4 and (2) a two identical cylinder system with diameters of 4.8 mm and 30 mm apart, and exposed to a shock wave moving a Mach number of 1.47. The computational results show excellent agreement with high-speed images and droplet deformation measured in the experiments. For both cases, it is found that the shock and the flow field in its wake leads to the flattening of the cylinder, followed by the formation of instability waves that are amplified by the baroclinic torque and the continuous reflections of the waves transmitted inside the liquid interior, eventually leading to ligament stripping. Based on the spatiotemporal evolution of the liquid and gaseous flowfields, time evolution of shock strength and parent droplet's mass and translation distance are also discussed.