Disentangling coherent structures and the origin of swirl-switching

Abstract

The physical origin of swirl-switching in turbulent bent-pipe flow remains the subject of ongoing research. We perform three direct numerical simulations (DNS) of flow through a $180^{\circ}$ bent pipe for curvature $\gamma=0.2$ at $Re_D=5,300$ and $Re_D=10,000$, and for curvature $\gamma=0.4$ at $Re_D=5,300$. Here, $Re_D$ is the Reynolds number based on the bulk velocity $U_b$ and pipe diameter $D$. The DNS data are subsequently used to conduct modal decompositions and local stability analysis (LSA). We discuss the limitations of common modal decomposition methods and introduce a new decomposition method, filtered Hilbert proper orthogonal decomposition (FHPOD), enabling us to isolate different instabilities as distinct FHPOD modes. FHPOD reveals seven modes belonging to four distinct families: a low-frequency axial mode, two swirl-switching modes, two swirl-breathing modes and a pair of downstream shear-layer modes. The swirl-switching and swirl-breathing modes are localised to the curved section of the bent-pipe flow and represent the sinuous and varicose instabilities of the Dean vortices, respectively. The DNS data are used to perform local stability analysis of the mean flow using the frozen eddy-viscosity method at the two streamwise wavenumbers associated with the two swirl-switching and swirl-breathing modes. The linear stability analysis reveals six unstable branches, with the swirl-switching mode being the most unstable branch. Another unstable branch represents the swirl-breathing mode. The modes obtained from the local stability analysis are in close agreement with their FHPOD counterparts in both spatial features and the range of Strouhal numbers. The results support the interpretation that swirl-switching arises as an intrinsic instability of the bent-pipe mean flow, which can be excited by incoming turbulent structures.