Dynamics of shock interaction with a curved Fast-Slow (F/S) gaseous interface

In oblique shock refraction through an interface, the shock incidence angle, the shock Mach number, the interface density ratio and the heat capacity ratio determine the refraction system. For a given gaseous interface and shock strength, regular refraction happens when the incidence angle is small. There exists a transition angle at which an irregular refraction will take place. Solutions of these refraction systems determine the local flow field. Macroscopically, such interactions play a role in shock bubble/droplet interactions, and finite amplitude Richtmyer-Meshkov (RM) problems, which are important in the design of propulsion systems. Interface morphology and circulation deposition are the key engineering quantity in these problems. Current analytical models have certain limitations: (1) They consider irregular refraction systems as power series expansion of regular refractions, which in fact has fundamental difference in circulation deposition mechanisms, (2) They consider only Steady-Pseudosteady refraction process, and (3) Interface morphology during the interaction is not considered.

The objective of this study is to consider shock refraction on a curved fast-slow interface for irregular refraction systems. We model the pseudosteady and unsteady behavior by developing a general model from Henderson's refraction analysis and Ben-Dor’s Skews’ theory for shock reflection and perturbation to bridge the limitations of current shock refraction model. We study unsteadiness of shock refraction induced by interface curvature, sudden geometry changes and diffusion of the interface. We first consider curved interface by a series of slanted planar interface, pseudosteady solution for regular and (irregular) Mach reflection refraction is solved and then apply unsteady corrections to pseudosteady by solving the shock dynamics at vicinity confluence point as it interacts with changing boundary conditions. The transition and termination of the Mach Reflection Refraction (MRR) system is also investigated in detail.

Our model, using basic principles of gas dynamics, is then verified by comparison to high-order-accurate numerical simulations