Numerical and theoretical analysis of shock wave interactions with abrupt area changes

Wave propagation in channels with area changes is a topic of significant practical interest that involves a rich set of coupled physics. While the acoustic wave problem has been studied extensively, the shock propagation problem has received less attention. In addition to its practical significance, this problem also introduces deep fundamental issues associated with how energy in propagating large-amplitude disturbances is redistributed upon interaction with inhomogeneities. This paper presents a study of shock scattering and entropy and vorticity coupling for shock wave propagation through discrete area changes. It compares results from computational fluid dynamics to those of one-dimensional quasi-steady calculations. The solution space is naturally divided into five ‘regimes’ based upon the incident shock strength and area ratio. This paper also presents perturbation methods to quantify the dimensionless scaling of physical effects associated with wave reflection/transmission and energy transfer to other disturbances. Finally, it presents an analysis of the ‘energetics’ of the interaction, quantifying how energy that initially resides in dilatational disturbances and propagates at the shock speed is redistributed into finite-amplitude reflected and transmitted waves as well as convecting vortical and entropy disturbances.