Publications - Benoît Pier

Do not take the name of root in vain.

Absolute instabilities in eccentric Taylor–Couette–Poiseuille flow

C. Leclercq, B. Pier and J. Scott

Laboratoire de mécanique des fluides et d'acoustique, École centrale de Lyon – CNRS – Université Claude-Bernard Lyon 1 – INSA, 36 avenue Guy-de-Collongue, 69134 Écully cedex, France

Journal of Fluid Mechanics 741, 543–566 (2014)

Abstract:

The effect of eccentricity on absolute instabilities (AI) in the Taylor–Couette system with pressure-driven axial flow is investigated. Five modes of instability are considered, characterised by a pseudo-azimuthal wavenumber m. They correspond to deformed toroidal (m=0) and left-/right-handed helical structures (m>0/m<0) made of one or two waves (|m|=1, 2). The most absolutely unstable mode always corresponds to Taylor-like vortices, with m=0. However, AI properties of other m are close for highly eccentric configurations, with large enough axial flow. Axial advection, characterised by a Reynolds number Re_z, carries perturbations away from their source, and has a strong stabilising effect on AI. On the other hand, the effect of eccentricity e is complex: increasing e generally delays AI, except for a range of moderate eccentricites 0.30 dominate for larger Re_z. The instability mechanism of AI is clearly centrifugal, even for the larger values of Re_z considered, as indicated by an energy analysis. For large enough Re_z , critical modes localise in the wide gap for low e, but their energy distribution is shifted towards the diverging section of the annulus for moderate e. For highly eccentric geometries, instabilities are controlled by the minimal annular clearance, and critical modes are confined in the vicinity of the inner cylinder. Untangling the AI properties of each m requires consideration of multiple saddle points for each dispersion relation.

doi:10.1017/jfm.2013.646

hal-00948589

2014a_leclercq_jfm.pdf