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Non-linear disturbance growth during sedimentation in dilute fibre suspensions
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-2906-9306
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Chemical Science and Engineering (CHE), Centres, Wallenberg Wood Science Center.
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.

Place, publisher, year, edition, pages
2013. Vol. 719, 268<-294 p.
Keyword [en]
particle/fluid flow, suspension, instability
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-98346DOI: 10.1017/jfm.2013.4ISI: 000315082000012Scopus ID: 2-s2.0-84874238181OAI: oai:DiVA.org:kth-98346DiVA: diva2:536854
Note

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

Available from: 2012-06-25 Created: 2012-06-25 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Eulerian Numerical Study of the Sedimentation of Fibre Suspensions
Open this publication in new window or tab >>Eulerian Numerical Study of the Sedimentation of Fibre Suspensions
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
Fokker-Planck equation, particle/fluid flow, suspension, instability
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-96767 (URN)978-91-7501-408-1 (ISBN)
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
2. Instability in Settling Fibres: A Numerical Study
Open this publication in new window or tab >>Instability in Settling Fibres: A Numerical Study
2014 (English)Doctoral 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 concentration instability under gravity at low Reynolds numbers. Initially well-mixed suspensions become inhomogeneous and anisotropic due to this instability. This project is focused on the development and validation of numerical models to understand the instability in a dilute fibre suspension by means of the mixture model and the point-particle model.

For periodic boundary condition, we use a linear stability analysis to show that inertia and hydro dynamic translational diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. However, numerical simulations indicate a weak wavenumber selection even at zero Reynolds number. Numerical simulations also show that the induced flow may either die or saturate on a finite amplitude. The characterof this long time behaviour is dictated by the wavenumber, the presence or absence of the translational diusivity, rotational diffusivity, and the fluid inertia on particle motions. Moreover, the most unstable wavenumber decreases with time and the maximum amplitude increases. The smallest wavenumber obtains the largest amplitude at steady state.

For a vessel bounded by sidewalls, the near-wall convection is an upward back flow in the very beginning, due to the combined effects of the steric-depleted layer and a hydrodynamiclly-depleted region near the wall. However, the evolution of the near-wall convection at later times depends on the aspect ratio of the bres, the translational diffusivity and the initial perturbations. The steric-depleted layer in the mixture model can be neglected for large widths. Multiple streamers are obtained due to the sidewalls, implying that the sidewalls can generate a wavelength which is smaller than the channel width. The suspension ends up with a single streamer on one side of the container, consistent with the results of the cases with periodic boundary condition but different from the experimental results. This might be due to the absence of the botton wall in the mixture model. Moreover, the global structure evolution of a suspension is dependent on the width of the vessel and the amplitude ofthe initial perturbations.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. xii, 41 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:01
Keyword
bre suspensions, sedimentation, instability, mixture model, point-particle mode
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-141037 (URN)978-91-7595-006-8 (ISBN)
Public defence
2014-02-21, Sal F3, Lindstedtsvägen 26, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20140207

Available from: 2014-02-07 Created: 2014-02-05 Last updated: 2014-02-07Bibliographically approved

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Dahlkild, Anders A.

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