Direct Numerical Simulations of Supersonic Interfacial Flows

Introduction

Gas-liquid interfaces, when subject to accelerations and/or velocity gradients, are unstable to infinitesimal perturbations—a classical subject that is well understood, mainly via linear theory, but individually for each class of such flows (Rayleigh- Taylor, Kelvin-Helmholtz, and Richtmeyer-Meshkov). Approximate, analytical, weakly non-linear and even non-linear methods exist for some cases, but again only for the rather idealized problems that involve accelerations normal to the interface or velocity gradients in flows parallel to the interface. While these inform qualitatively about systems found in practice, absent are understanding and capability to treat superposition of mechanisms in arbitrary flows, as for example those arising in the presence of accelerating, oblique or curved interfaces.More severely, absent are such methods that can accommodate compressible and shock-wave-bearing flows. This is the subject addressed by the numerical work summarized in this paper—the supporting experiments were carried out in a large-scale shock tube, they include Newtonian as well as viscoelastic liquids, and the quantification includes the resulting particle size distributions [1]. The canonical problem is aerobreakup of liquid drops [1], and applications of significant current interest include de-icing of airplane wings, internal-combustion, rocket, and pulse-detonation engines, and dissemination of liquid agents in the atmosphere.