Three-dimensional wake transitions in the flow around a twisted cylinder

Abstract

The three-dimensional (3D) wake transition process of a twisted cylinder is investigated using Floquet stability analysis and 3D direct numerical simulation. Floquet stability analysis is conducted on elliptic cross-sections to examine the influence of rotation phase angle on the onset of 3D instabilities. The critical Reynolds numbers (Re) for the onset of 3D instabilities vary evidently along the spanwise direction of a twisted cylinder, whereas the corresponding critical wavelengths remain relatively consistent, independent of rotation angles. Both the critical values of Re and wavelength exhibit spanwise symmetry within a geometric wavelength of the twisted cylinder. The critical unstable modes are concentrated within vortex cores and display odd reflection-translation symmetry. The similarities in temporal and spatial characteristics identify these dominant Floquet modes as Mode-A-type instabilities. At low Reynolds numbers, the 3D shedding modes are stabilized when their spanwise wavelength coincides with that of the twisted geometry. However, the shedding patterns with “lock-in” wavelength disappear at a higher Re. Due to the variations in the critical Reynolds numbers along the span, regions of instability emerge locally before spreading with increasing Re. The large wavelength of the modes induces the expanding tendency and intersection with neighbouring vortex pairs, ultimately giving rise to vortex dislocations in the wake of a twisted cylinder.