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Buoyancy-induced turbulence in a tilted pipe

Published online by Cambridge University Press:  08 December 2014

Yannick Hallez  and
Jacques Magnaudet
Yannick Hallez
Affiliation:
Université de Toulouse; INPT, UPS; LGC (Laboratoire de Génie Chimique); 118 route de Narbonne, F-31062 Toulouse, France CNRS; LGC; F-31030 Toulouse, France
Jacques Magnaudet*
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France CNRS; IMFT; F-31400 Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

Numerical simulation is used to document the statistical structure and better understand energy transfers in a low-Reynolds-number turbulent flow generated by negative axial buoyancy in a long circular tilted pipe under the Boussinesq approximation. The flow is found to exhibit specific features which strikingly contrast with the familiar characteristics of pressure-driven pipe and channel flows. The mean flow, dominated by an axial component exhibiting a uniform shear in the core, also comprises a weak secondary component made of four counter-rotating cells filling the entire cross-section. Within the cross-section, variations of the axial and transverse velocity fluctuations are markedly different, the former reaching its maximum at the edge of the core while the latter two decrease monotonically from the axis to the wall. The negative axial buoyancy component generates long plumes travelling along the pipe, yielding unusually large longitudinal integral length scales. The axial and crosswise mean density variations are shown to be respectively responsible for a quadratic variation of the crosswise shear stress and density flux which both decrease from a maximum on the pipe axis to near-zero values throughout the near-wall region. Although the crosswise buoyancy component is stabilizing everywhere, the crosswise density flux is negative in some peripheral regions, which corresponds to apparent counter-gradient diffusion. Budgets of velocity and density fluctuations variances and of crosswise shear stress and density flux are analysed to explain the above features. A novel two-time algebraic model of the turbulent fluxes is introduced to determine all components of the diffusivity tensor, revealing that they are significantly influenced by axial and crosswise buoyancy effects. The eddy viscosity and eddy diffusivity concepts and the Reynolds analogy are found to work reasonably well within the central part of the section whereas non-local effects cannot be ignored elsewhere.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulent convection Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 762 , 10 January 2015 , pp. 435 - 477
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Copyright
© 2014 Cambridge University Press 

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Hallez and Magnaudet supplementary movie

Flow development along the pipe. The coloured surfaces represent iso-contours of C. They are distributed evenly between C=0.1 (red) and C=0.9 (blue), with green corresponding to C=0.5.

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Hallez and Magnaudet supplementary movie

Detail of the flow development in the upper part of the pipe visualized with the C=0.1 iso-surface. The latter is coloured by the "swirling strength" intensity which helps identify three-dimensional vortical structures (see Hallez & Magnaudet (2008) and references therein).

Download Hallez and Magnaudet supplementary movie(Video)
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