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Numerical investigation of three-dimensional fiber suspension flow by using finite volume method

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Abstract

Fiber suspension flow is common in many industrial processes like papermaking and fiber-reinforcing polymer-based material forming. The investigation of the mechanism of fiber suspension flow is of significant importance, since the orientation distribution of fibers directly influences the mechanical and physical properties of the final products. A numerical methodology based on the finite volume method is presented in the study to simulate three-dimensional fiber suspension flow within complex flow field. The evolution of fiber orientation is described using different formulations including FT model and RSC model. The pressure implicit with splitting of operators algorithm is adopted to avoid oscillations in the calculation. A laminate structure of fiber orientation including the shell layer, the transition layer and the core layer along radial direction within a center-gated disk flow channel is predicted through a three-dimensional simulation, which agrees well with Mazahir’s experimental results. The evolution of fiber orientation during the filling process within the complex flow field is further discussed. The mathematical model and numerical method proposed in the study can be successfully adopted to predict fiber suspension flow patterns and hence to reveal the fiber orientation mechanism.

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Abbreviations

\( \varvec{p} \) :

Fiber orientation vector

\( \varvec{u} \) :

Velocity vector

\( \nabla \) :

Hamilton differential operator

\( \dot{\varvec{p}} \) :

Fiber angular velocity vector

\( \varvec{w} \) :

Vorticity tensor

\( \varvec{d} \) :

Deformation rate tensor

\( C_{I} \) :

Interaction coefficient

\( \dot{\gamma } \) :

Shear rate

\( \lambda \) :

Particle geometrical parameter

\( \varvec{a} \) :

Second-order orientation tensor

\( \varvec{A} \) :

Fourth-order orientation tensor

\( \kappa \) :

Strain reduction factor

\( \rho \) :

Material density

\( \varvec{\tau} \) :

Extra stress tensor

\( p \) :

Hydrostatic pressure

\( c_{p} \) :

Heat capacity

\( k \) :

Heat conductivity

\( \eta_{n} \) :

Non-Newtonian viscosity

\( N_{p} \) :

Particle number

\( \varphi \) :

Volume fraction

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Acknowledgements

This work is financially supported by the Natural Science Foundation of China (No. 51675308), the Natural Science Foundation of China (No. 51205231) and the Natural Science Foundation of Shandong Province (No. ZR2012EEQ001).

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Authors and Affiliations

  1. Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan, 250061, Shandong, People’s Republic of China

    Yue Mu, Guoqun Zhao, Yifan Liu, Yining Song & Chao Sun

  2. Engineering Research Center for Mould & Die Technologies, Shandong University, Jinan, 250061, Shandong, People’s Republic of China

    Yue Mu, Guoqun Zhao, Anbiao Chen, Yifan Liu, Yining Song & Chao Sun

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  1. Yue Mu
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  2. Guoqun Zhao
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  3. Anbiao Chen
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  4. Yifan Liu
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  5. Yining Song
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Correspondence to Yue Mu or Guoqun Zhao.

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Mu, Y., Zhao, G., Chen, A. et al. Numerical investigation of three-dimensional fiber suspension flow by using finite volume method. Polym. Bull. 74, 4393–4414 (2017). https://doi.org/10.1007/s00289-017-1960-z

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  • DOI: https://doi.org/10.1007/s00289-017-1960-z

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