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Modelling the Fibre Anisotropy Profile in Shear Layers Leaving a Planar Contraction
Metso Paper Karlstad AB, Karlstad, Sweden .
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-2906-9306
2010 (English)In: Paper Conference and Trade Show 2010, PaperCon 2010: Volume 3, 2010, 2320-2353 p.Conference paper, Published paper (Refereed)
Abstract [en]

The fibre orientation state evolution is evaluated by the fully 3D convection-dispersion equation, i.e. the Fokker-Planck equation. This is solved along various streamlines in the contraction with vane inserts so that effects of wakes and boundary layers could be studied across a jet. As an input to the fibre orientation model the turbulent flow field is solved by Computational Fluid Dynamics (CFD) with second-order closure of the turbulence model. Parameter values for the rotational dispersion coefficient of three hypotheses reported in studies are tested for an independent experimental case. After the contraction the anisotropy profile across the flow, has a variation in anisotropy value in different regions, identified as the boundary layer, the undisturbed region and wakes. The numerical result predicts these regions by comparison to the experimental result with the fully 3D approach of the fibre orientation state applied.

Place, publisher, year, edition, pages
2010. 2320-2353 p.
Keyword [en]
Convection-dispersion equations, Dispersion coefficient, Fibre orientation, Numerical results, Parameter values, Second-order closure, Shear layer, State evolutions
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-8485Scopus ID: 2-s2.0-78449244694ISBN: 978-161738789-0 (print)OAI: oai:DiVA.org:kth-8485DiVA: diva2:13821
Conference
Paper Conference and Trade Show 2010, PaperCon 2010; Atlanta, GA; United States; 2 May 2010 through 5 May 2010
Note

QC 20100812. Uppdaterad från submitted till konferensbidrag (20100812).

Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2014-09-10Bibliographically approved
In thesis
1. Fibre Orientation Modelling Applied to Contracting Flows Related to Papermaking
Open this publication in new window or tab >>Fibre Orientation Modelling Applied to Contracting Flows Related to Papermaking
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The main goal of this work was to develop numerical models for studying the behaviour of fibres in an accelerated flow. This is of special interest for e.g. papermaking. The early stage of the paper manufacturing process determines most of the final properties of a paper sheet. The complexity of studying the flow of fibre suspensions both experimentally and numerically emphasises a need for new ideas and developments.

By means of solving the evolution of a convective-dispersion equation, i.e. the Fokker-Planck equation, a fully 3D approach with respect to the position and the two fibre angles, polar and azimuthal angles, following a streamline is presented. As an input to the fibre orientation model the turbulent flow field is solved by Computational Fluid Dynamics (CFD) with second-order closure in the turbulence model. In this work two new hypotheses have been presented for the variation of the non-dimensional rotational diffusivity with non-dimensional fibre length, Lf /η and the Reynolds number based on the Taylor micro-scale of the turbulence, Reλ Parameters for the two new hy- potheses and earlier models are determined with the aim of achieving a general relation and a value of the rotational dispersion coeffcient of stiff fibres in an anisotropic turbulent fluid flow. Earlier modelling work has been focused on solving the planar approach, i.e. assuming all fibres to be in one plane. This planar approach is discussed and compared with the fully 3D approach and its validity is evaluated.

The optimization of parameters for the different hypotheses correlated on a central streamline, showed a good agreement with an independent experimental result in the undisturbed region. Moreover, it is particularly interesting that the boundary layer region and the wake region are predicted fairly well and the phenomena are well described, which has not been the case earlier. It seems that the new hypothesis based on the variation of the non-dimensional fibre length, Lf /η gives the best correlation in these shear-layer regions. Further- more it was established that the planar approach fails to predict shear layers, i.e. the boundary layer and the wake regions. As emphasized in the theory section, the planar formulation is strictly valid only if all fibres are oriented in one plane, which is not the case in the shear layers. In the undisturbed region, the 3D and the planar approaches, agree in their results. This leads to the conclusion that both approaches are suitable when shear layers are not studied.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. x, 36 p.
Series
Trita-MEK, ISSN 0348-467X ; 2008:03
Keyword
Fokker-Planck, fibre orientation, shear flow, fibre suspension, planar contraction, headbox, turbulent flow
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-4762 (URN)
Public defence
2008-06-05, Sal L1, KTH, Drottning Kristinas väg 30, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20100812Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2010-08-12Bibliographically approved
2. On fibre suspension flow modelling: mechancal fibre flocculation and fibre orientation
Open this publication in new window or tab >>On fibre suspension flow modelling: mechancal fibre flocculation and fibre orientation
2005 (English)Licentiate thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH, 2005. 19 p.
Series
Trita-MEK, ISSN 0348-467X ; 2005:5
Keyword
Engineering physics, Teknisk fysik
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:kth:diva-344 (URN)
Presentation
2005-04-11, Sal L1, Drottning Kristinas väg 30, Stockholm, 10:15
Supervisors
Note
QC 20101202Available from: 2005-08-01 Created: 2005-08-01 Last updated: 2010-12-02Bibliographically approved

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Dahlkild, Anders

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