Approaching zero curvature: modal instability in a bent pipe

• Canton et al. [J. Fluid Mech. 792:894–909 (2016)] showed that the flow in a toroidal pipe is linearly unstable for any pipe curvature δ greater than 0.002. The same authors later provided a detailed characterisation of the laminar steady flow, reporting lower limits for the influence of the pipe curvature [Canton et al. Int. J. Heat Fluid Fl. 66:95-107 (2017)]. The objective of the present work is to investigate the behaviour of the linear instability as the curvature of the pipe tends to zero. Results indicate that the toroidal pipe remains linearly unstable for curvatures as low as 10−7. While the critical Reynolds number Re necessary for the instability grows with an approximately algebraic trend below δ = 0.002, the neutral curve also closes in onto the limit of negligible curvature. It therefore appears that there could be values of δ and Re where a linearly unstable toroidal flow could be connected to the linearly stable straight pipe flow.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)

Publication and Content Type

vet (subject category)

rap (subject category)