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Fibre Orientation Modelling Applied to Contracting Flows Related to Papermaking
KTH, School of Engineering Sciences (SCI), Mechanics.
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 [en]
Fokker-Planck, fibre orientation, shear flow, fibre suspension, planar contraction, headbox, turbulent flow
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-4762OAI: oai:DiVA.org:kth-4762DiVA: diva2:13823
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
List of papers
1. Modelling the effect of shear flow on fibre orientation anisotropy in a planar contraction
Open this publication in new window or tab >>Modelling the effect of shear flow on fibre orientation anisotropy in a planar contraction
Show others...
2007 (English)In: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 22, no 3, 376-382 p.Article in journal (Refereed) Published
Abstract [en]

The effect of turbulence generating vanes and its location in a planar contraction on fibre orientation anisotropy was studied by mathematical modelling. We use single phase CFD (Computational Fluid Dynamic) modelling as an input for the fibre orientation dispersion model to study the effect of shear flow and turbulence in an accelerated fluid flow on fibre orientation anisotropy. For different streamlines in the contracting channel, the fibre orientation distribution model is solved, and the fibre orientation anisotropy could be studied along streamlines near the vane wall and vane tip and further away downstream. The boundary layer did decrease the fibre orientation anisotropy both in the plane of paper and in the plane of contraction, i.e the fibres were less oriented. For the outlet profile of the contraction the fibre orientation anisotropy was more effected by the blunt vane tip than the tapered one. Experimental results in the literature were used to validate this modelling approach and a good qualitative agreement was achieved.

Keyword
fibre; orientation; anisotropy; turbulence; dispersion; modelling
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-8482 (URN)000250025000014 ()2-s2.0-34948865620 (Scopus ID)
Note
QC 20100812 Uppdaterad från konferensbidrag till artikel(20101202). Tidigare titel: Modelling a turbulent dilute fibre suspension in a planar contraction: Effect of vane types, vane position and wall boundary layer on fibre orientation distribution.Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2017-12-14Bibliographically approved
2. Study of the rotational diffusivity coefficient of fibres in planar contracting flows with varying turbulence levels
Open this publication in new window or tab >>Study of the rotational diffusivity coefficient of fibres in planar contracting flows with varying turbulence levels
2008 (English)In: International Journal of Multiphase Flow, ISSN 0301-9322, E-ISSN 1879-3533, Vol. 34, no 9, 894-903 p.Article in journal (Refereed) Published
Abstract [en]

The Fokker-Planck equation is solved by describing the evolution of a 3D fibre orientation state along a planar contraction. A constant value of the effective rotational diffusion coefficient was determined for four different turbulent flow cases in planar contractions, reported experimentally in the literature. Two hypotheses for the non-dimensional rotational diffusivity are presented, each based on two different turbulent time scales, i.e. the Kolmogorov time scales and the time scale associated with large energy bearing eddies. These hypotheses are dependent on either the Reynolds number, based on the Taylor micro-scale, and/or a non-dimensional fibre length. The hypothesis, based on the assumption of long fibres, L-t/n greater than or similar to 25, compared to the Kolmogorov scale and in the limit of large Re-lambda seems to capture the basic trends presented in the literature. This hypothesis has also the feature of predicting effects of varying fibre length within certain limits. Accordingly, by modeling the variation of turbulent quantities along the contraction in a CFD analysis, local values of rotational diffusivity can be evaluated with the mentioned hypothesis, based on either Kolmogorov time scale or Eulerian integral time scale.

Keyword
Fokker-Planck equation; fibre; orientation; anisotropy; turbulence; dispersion; modelling
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-8483 (URN)10.1016/j.ijmultiphaseflow.2008.02.005 (DOI)000259069300008 ()2-s2.0-47749133811 (Scopus ID)
Note
QC 20100812. Uppdaterad från in press till published (20100812).Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2017-12-14Bibliographically approved
3. Evolution of the Rotational Diffusivity Coefficient of Fibres along the Centreline of Turbulent Planar Contracting Flows
Open this publication in new window or tab >>Evolution of the Rotational Diffusivity Coefficient of Fibres along the Centreline of Turbulent Planar Contracting Flows
(English)Article in journal (Other academic) Submitted
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-8484 (URN)
Note
QS 20120327Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2012-03-27Bibliographically approved
4. Modelling the Fibre Anisotropy Profile in Shear Layers Leaving a Planar Contraction
Open this publication in new window or tab >>Modelling the Fibre Anisotropy Profile in Shear Layers Leaving a Planar Contraction
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.

Keyword
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:nbn:se:kth:diva-8485 (URN)2-s2.0-78449244694 (Scopus ID)978-161738789-0 (ISBN)
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
5. Comparison between Planar and Fully 3D Approaches for the Evolution of Fibre Orientation in the Shear Layers of Planar Contractions
Open this publication in new window or tab >>Comparison between Planar and Fully 3D Approaches for the Evolution of Fibre Orientation in the Shear Layers of Planar Contractions
(English)Article in journal (Other academic) Submitted
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-8486 (URN)
Note
QS 20120327Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2012-03-27Bibliographically approved

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