Symmetry breaking, ring formation and other phase boundary structures in shock tube experiments on retrograde fluids

Abstract

A peculiar multi-dimensional wave pattern in shock tube experiments on retrograde fluids is the ring formation phenomenon. When the incident shock is reflected by the endwall of a shock tube filled with retrograde fluid vapour, under certain conditions, rings of liquid/vapour mixture form behind the reflected shock. In this paper, we find the reason for such symmetry breaking and ring formation phenomena by studying a prototype model for flows with liquid/vapour phase transitions. The isothermal case of this model exhibits all major one-dimensional wave patterns observed in shock tube experiments on retrograde fluids. The symmetry is broken by the liquid or liquid/vapour drops initiated behind the reflected shock where the pressure is higher than the equilibrium pressure. Liquid drops become liquid/vapour mixture drops later. Using a liquid/vapour mixture drop at the reflecting wall as the initial condition for the prototype model, it is shown that this drop will evolve into a ring, yielding the explanation for ring formation. The outer fronts of rings are collapsing waves. Such waves are supersonic, as confirmed by some photographs of actual experiments. It is also shown that a liquid or liquid/vapour mixture drop cannot evolve into a ring if no reflecting wall is present, agreeing with experimental observation. A mechanism is also provided by the model for the emergence of the ‘button’ at the centre of, and the small-scale asperities at, the liquefaction shock front observed at the exit of the open-end shock tube.