Subcritical versus supercritical transition to turbulence in curved pipes Journal Article


Author(s): Kühnen, Jakob; Braunshier, P; Schwegel, M; Kuhlmann, Hendrik C; Hof, Björn
Article Title: Subcritical versus supercritical transition to turbulence in curved pipes
Affiliation IST Austria
Abstract: Transition to turbulence in straight pipes occurs in spite of the linear stability of the laminar Hagen-Poiseuille flow if both the amplitude of flow perturbations and the Reynolds number Re exceed a minimum threshold (subcritical transition). As the pipe curvature increases, centrifugal effects become important, modifying the basic flow as well as the most unstable linear modes. If the curvature (tube-to-coiling diameter d/D) is sufficiently large, a Hopf bifurcation (supercritical instability) is encountered before turbulence can be excited (subcritical instability). We trace the instability thresholds in the Re - d/D parameter space in the range 0.01 ≤ d/D\ ≤ 0.1 by means of laser-Doppler velocimetry and determine the point where the subcritical and supercritical instabilities meet. Two different experimental set-ups are used: a closed system where the pipe forms an axisymmetric torus and an open system employing a helical pipe. Implications for the measurement of friction factors in curved pipes are discussed.
Keywords: Transition to turbulence; instability; bifurcation
Journal Title: Journal of Fluid Mechanics
Volume: 770
ISSN: 1469-7645
Publisher: Cambridge University Press  
Date Published: 2015-01-01
Start Page: Article number: 770 R3
DOI: 10.1017/jfm.2015.184
Notes: The project was partially funded by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC grant agreement 306589. J.K. acknowledges the provision of preliminary numerical data by P. Schlatter and A. Noorani of KTH Mechanics related to this work and friendly support by G. Lemoult.
Open access: no