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Study of the rotational diffusivity coefficient of fibres in planar contracting flows with varying turbulence levels
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-2906-9306
2008 (English)In: International Journal of Multiphase Flow, ISSN 0301-9322, 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.

Place, publisher, year, edition, pages
2008. Vol. 34, no 9, 894-903 p.
Keyword [en]
Fokker-Planck equation; fibre; orientation; anisotropy; turbulence; dispersion; modelling
National Category
Other Materials Engineering
URN: urn:nbn:se:kth:diva-8483DOI: 10.1016/j.ijmultiphaseflow.2008.02.005ISI: 000259069300008ScopusID: 2-s2.0-47749133811OAI: diva2:13819
QC 20100812. Uppdaterad från in press till published (20100812).Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2010-08-12Bibliographically 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.
Trita-MEK, ISSN 0348-467X ; 2008:03
Fokker-Planck, fibre orientation, shear flow, fibre suspension, planar contraction, headbox, turbulent flow
National Category
Other Materials Engineering
urn:nbn:se:kth:diva-4762 (URN)
Public defence
2008-06-05, Sal L1, KTH, Drottning Kristinas väg 30, Stockholm, 10:00
QC 20100812Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2010-08-12Bibliographically approved

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