Numerical study on instabilities behind a circular disk in a uniform flow

摘要

Instabilities behind a circular disk, which is normal to a uniform free-stream with aspect ratio of χ = 5. are numerically studied in the range of Re from 115 to 1000. The onsets of three characteristic instabilities including natural vortex shedding, shear-layer instability and a very low frequency instability, which are associated with the Reynolds number, are reported. When Re＜ 152, the wake stays steady and no vortex shedding occurs. A regular bifurcation leading to two-thread wake is observed for Re from 120 to 152. When Re increases to 152, the hairpin vortices begin to be periodically shed in a regular pattern. A reflectional-symmetry-breaking (RSB) mode is observed for Re from 152 to 155, a standing-wave (SW) mode is captured for Re from 156 to 247, and an unsteady state with planar symmetry and non-zero mean lift is captured for Re from 248 to 264. It is found that the hairpin vortices are always shedding in a fixed orientation for RSB mode, while shedding from diametrically opposite orientations at SW mode and the unsteady state with planar symmetry and non-zero mean lift. When Re increases to 265, a low frequency instability attributed to the irregular rotation of vortex shedding location is observed. The hairpin vortices are periodically shed in an irregular pattern and a new '4L' vortex formation mode is identified. When Re increases to 650, the shear-layer instability starts to be detected in the shear layer. The critical Reynolds number is firstly identified in the range of 601-650. The cylindrical shear layer surrounding the vortex formation zone rolls up to form oblate ring vortices. The hairpin vortices break into pieces and small-scale vortices associated with the shear-layer instability are observed.