Three-dimensional transition of vortex shedding flow around a circular cylinder at right and oblique attacks

Abstract

Vortex shedding from an inclined circular cylinder at low values of Reynolds number (Re) is investigated numerically. The aim of the study is to investigate the effect of cylinder oblique angle on the transition from two-dimensionality (2D) to three-dimensionality (3D) of the wake flow. The Navier-Stokes equations are solved by the Petrov-Galerkin finite element method for Reynolds numbers ranging from 100 to 1000 and the flow attack angles of α = 0° and 45°. For the right attack angle case (α = 0°), the predicted wavy spanwise vortices in the early stage of the transition mode A, the vortex dislocation in the late stage of the transition mode A and the streamwise-vortex dominant wake flow structure in the transition mode B are found to agree well with independent experimental observations and measurements. The transition from 2D to 3D at α = 45° was found distinctively different from that at α = 0°. For α = 45°, no clear-cut transition modes are observed. The wake is characterized by wavy spanwise vortices close to the lower boundary of the transition Reynolds number regime, which are similar to those in the early stage of the transition mode A at α = 0°. The vortex-dislocation in the transition mode A was not observed at α = 45°. It appears that the fluid flow in the spanwise direction in the primary vortices at α = 45° does not allow the instability to sustain at a specific spanwise location and trigger the vortex dislocation. Although the wake flow structure is different, the variation of the normal Strouhal number with the normal Reynolds number (both based on the velocity component perpendicular to the cylinder span) at α = 45° is close to that at α = 0° in the transitional Reynolds number regime. The root mean square of the lift coefficient normalized by the velocity component perpendicular to the axial direction of the cylinder at α = 45° is about 20% to 25% larger than that at α = 0° in the Reynolds number regime between 250 and 500.