Secondary instability of channel-confined transition around dual-circular cylinders in tandem

Abstract

Abstract The incompressible viscous flows around the dual-circular cylinders in tandem confined in a plane channel were simulated by direct numerical simulations (DNS) with the Reynolds numbers (Re) at 200, 400 and 800. The blocking ratio and cylinder center-to-center distance are set at 1 / 4 and 2.5. The secondary instabilities and the corresponding vortex evolution in transition were investigated by the dynamics of third-generation vortex identification quantities of liutex scalar and vector, which are governed by the vorticity transport equations, or Helmholtz equations, and the liutex-shear decomposition. The studies, for the first time, discover the influence of liutex stretching effect on the rigid rotating strength, which gives rise to the two-dimensional non-uniform deformations of the liutex isosurface in the secondary transition. The simulations also demonstrate that the liutex vector is mainly produced by the newly-defined shear allocating effect at the early stage of vortex generation. The quasi-streamwise vortices in the entire flow domain are found being generated in the region where the shear presents a strong strength. With the distinctive elliptic instability in nature, the vortices in the gap are confined by the cylinder shear layers for the Re=400 flow and the vortex bulges structures are firstly observed as the start to transit from the 2-D transient vortex to the more complex 3-D vortical structures in gap, namely the secondary instability. In the wake region, the study reported the two prominent developing stages of Mode B vortex pairs corresponding to the shear instability and vortex stretching, which are governed by their own corresponding balancing mechanisms in the liutex vector dynamic equations. The similar two-stages developing processes are also confirmed in the bluff-body wake transitions with the Mode B instability in nature. With the increase of Re, the shear layers start to interact with the gap vortices and the new secondary-instability is found causing by the hairpin vortices, which are originated from the gap and subsequently lead to the rapid three-dimensional transitions in both gap and wake regions. These studies of vortex structures and dynamics push the front of the current understandings regarding the secondary instability and the subsequent transition to fully-developed turbulence.