Scaling vortex breakdown mechanism based on viscous effect in shock cylindrical bubble interaction

Abstract

In shock accelerated flows such as supersonic injection, it is normally recognised that flow structures are well scaled by the characteristic length under the continuity hypothesis. By investigating the interaction between the incident shock and cylindrical bubbles ranging from dozens of millimetres to dozens of micrometres, a breakdown of the vortex formation is observed within the Navier-Stokes-suitable scale. The vortex breakdown phenomenon characterised by the specific stretching factor is directly reflected by the decline in normalised circulation. Further insight into the physical mechanism of decreased circulation reveals that the effect of viscous dissipation against baroclinic production is intensified in microscale interactions. In order to measure the extent of vortex breakdown, a dimensionless scaling vortex breakdown number μ*, which reflects the competing contribution from dissipation and baroclinicity, is proposed through order-of-magnitude analysis. According to the viscous effect on the vortex formation, μ* is classified under three flow regimes exhibiting different vorticity dynamics (μ* < 10−3, 10−3 < μ* < 10−1, and μ* > 10−1, which indicates inviscid, transient, and viscous regimes, respectively). In nature, the introduction of the nonlinear factor such as viscous dissipation in flow development causes the scaling breakdown, where the accurate modeling and simulation of the nonlinear factor are the core challenges in understanding the microscale dynamics.