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Instability in Settling Fibres: A Numerical Study
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
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 [en]
bre suspensions, sedimentation, instability, mixture model, point-particle mode
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-141037ISBN: 978-91-7595-006-8 (print)OAI: oai:DiVA.org:kth-141037DiVA: diva2:694152
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
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. Nonlinear interactions of multiple modes and spectral analysis of a suspension of settling fibres
Open this publication in new window or tab >>Nonlinear interactions of multiple modes and spectral analysis of a suspension of settling fibres
(English)Manuscript (preprint) (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-141034 (URN)
Note

QS 2014

Available from: 2014-02-05 Created: 2014-02-05 Last updated: 2014-02-07Bibliographically approved
3. Numerical simulations of the sedimentationin dilute fibre suspensions
Open this publication in new window or tab >>Numerical simulations of the sedimentationin dilute fibre suspensions
Show others...
2013 (English)Conference paper, Oral presentation only (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-141030 (URN)
Conference
icmf2013
Note

QC 20140207

Available from: 2014-02-05 Created: 2014-02-05 Last updated: 2014-02-07Bibliographically approved
4. Near-wall convection in a sedimenting suspension of fibres
Open this publication in new window or tab >>Near-wall convection in a sedimenting suspension of fibres
(English)Manuscript (preprint) (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-141035 (URN)
Note

QS 2013

Available from: 2014-02-05 Created: 2014-02-05 Last updated: 2014-02-07Bibliographically approved
5. Effects of walls and perturbations on the sedimentation in fibre suspensions
Open this publication in new window or tab >>Effects of walls and perturbations on the sedimentation in fibre suspensions
(English)Manuscript (preprint) (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-141036 (URN)
Note

QS 2013

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

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