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Eulerian Numerical Study of the Sedimentation of Fibre Suspensions
KTH, School of Engineering Sciences (SCI), Mechanics.
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

 Sedimenting suspensions exist in a varity of natural phenomena and industrial applications. It is already observed in experiments that the dilute fibre suspensions experience a hydrodynamics instability under gravity at low Reynolds numbers. Initially well-mixed suspensions become inhomogeneous and anisotropic due to this instability.The main goal of this work is to understand the instability in a dilute fibre suspension by means of an Eulerian approach which is based on the Navier-Stokes equations coupled to Fokker-Planck equation for the PDF of fibres.Using a linear stability analysis, we show that inertia and hydrodynamic translational diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. For small, but finite Reynolds number of the fluid bulk motion, the most unstable wavenumber is a finite value which increases with Reynolds number, and where the diffusion narrows the range of unstable wavenumbers. With periodic boundary conditions, numerical simulations of the full non-linear evolution in time of a normal mode perturbation show that the induced flow may either die or saturate on a finite amplitude. The character of this long time behaviour is dictated by the wavenumber and the presence or absence of the translational and rotational diffusivities.In a simulation domain confined by vertical walls, a series of alternating structures of risers and streamers emerge continuously from the walls until they meet in the middle of the domain. For moderate times, this agrees qualitatively with experimental and theoretical results. Moreover, our simulation in a vessel of infinite height obtained an increasing wavelength evolution due to the congregation of the streamers or risers. In the end, there is constantly only one streamer left, and it drifts randomly to one side of the container until the evolution reaches a steady state. It is also found that the perturbations added to the initial conditions can induce more high density regions whose sizes and velocities are strongly linked to the initial perturbations of the number density or the flow field. In addition, the maximum number of streamers increases with Reynolds number, volume fraction and channel width.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. , v, 25 p.
Series
Trita-MEK, ISSN 0348-467X ; 2012:13
Keyword [en]
Fokker-Planck equation, particle/fluid flow, suspension, instability
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-96767ISBN: 978-91-7501-408-1 (print)OAI: oai:DiVA.org:kth-96767DiVA: diva2:532594
Presentation
2012-06-15, V3, Teknikringen 72, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20120625Available from: 2012-06-25 Created: 2012-06-11 Last updated: 2012-06-25Bibliographically approved
List of papers
1. Non-linear disturbance growth during sedimentation in dilute fibre suspensions
Open this publication in new window or tab >>Non-linear disturbance growth during sedimentation in dilute fibre suspensions
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 719, 268<-294 p.Article in journal (Refereed) Published
Abstract [en]

Disturbances in a dilute fibre suspension is studied with an Eulerian approach. Based on a linear stability analysis, it is shown that inertia and hydrodynamic diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. For small, but finite Reynolds number of the fluid bulk motion, the most unstable wavenumber is a finite value which increases with Reynolds number, and where the diffusion narrows the range of unstable wavenumbers. Numerical simulations of the full non-linear evolution in time of a normal mode perturbation show that the induced flow may either die or saturate on a finite amplitude. The character of this long time behaviour is dictated by the wavenumber and the presence or absence of the translational and rotational diffusivities.

Keyword
particle/fluid flow, suspension, instability
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-98346 (URN)10.1017/jfm.2013.4 (DOI)000315082000012 ()2-s2.0-84874238181 (Scopus ID)
Note

 Updated from "Manuscript" to "Article". QC 20140207

Available from: 2012-06-25 Created: 2012-06-25 Last updated: 2017-12-07Bibliographically approved
2. Evolution of streamers in sedimentation of fibre suspensions bounded by vertical walls
Open this publication in new window or tab >>Evolution of streamers in sedimentation of fibre suspensions bounded by vertical walls
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The simulation, based on the Navier-Stokes equations coupled to a transport equation for the PDF of fibres, shows that a series of alternating structures of risers and streamers emerge continuously from the walls until they meet in the middle of the domain. For moderate times, this agrees qualitatively with experimental and theoretical results. Moreover, our simulation in a vessel of infinite height obtained an increasing wavelength evolution due to the congregation of the streamers or risers. In the end, there is constantly only one streamer left, and it drifts randomly to one side of the container until the evolution reaches a steady state. It is also found that the perturbations added to the initial conditions can induce more high density regions which sizes and velocities are strongly linked to the initial perturbations of the number density or the flow field. In addition, the maximum number of streamers increases with Reynolds number, volumefraction and channel width.

Keyword
particle/fluid flow, suspension, instability
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-98396 (URN)
Note
QC 20120625Available from: 2012-06-25 Created: 2012-06-25 Last updated: 2012-06-25Bibliographically approved

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Citation style
  • apa
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Output format
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