Internal vortex breakdowns with stair-step change in rotating flows

Abstract

Understanding internal vortex breakdowns (VBs) and their trajectories in sealed cylinders are important for the scientific and industrial applications with which they are linked. However, the fluids in sealed cylinders are often sheared, which makes it difficult to clearly and multidirectionally observe their internal flow patterns simultaneously with existing experimental tools; this results in some important features not being captured. In this work, we performed thousands of numerical simulations in a sealed cylinder utilizing the finite element approach. Abundant internal VB patterns were obtained for different aspect ratios as the Reynolds number ( Re) increased. To further quantitatively study the morphological evolution of VBs, we focused on the axial lengths and trajectories of VBs with multiple aspect ratios. Surprisingly, the numbers of VBs in the rotating fluid were not fixed for the same aspect ratio, which also affected the complexity of the VB evolution. In particular, the stair-step changes of the locations of the VB and local extrema of the axial velocity, pressure, and vorticity of the key flows at the axis were revealed in detail. We used the theory of swirl decay to explain the VB formation and stair-step change from an energy perspective and clarified why the pressure minimum was under the center of the VB. The discovery of the stair-step change of the VB provided evidence of the existence of a new class of fluid behavior that may provide insight into vortex control.