Doktorsdisputation
Instability in Settling Fibres: A Numerical Study
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| Respondent |
Huvudhandledare |
Bihandledare |
Datum |
| Feng Zhang |
Anders Dahlkild |
Fredrik Lundell |
2014-02-21 |
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| Opponent |
| Mark Martinez, University of British Columbia
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| Betygsnämd |
Srdjan Sasic, Chalmers University of Technology
Anna-Karin Tornberg, Kungliga Tekniska Högskolan
Tomas Wikström, Metso Paper Inc., Sundsvall
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AbstractSedimenting suspensions exist in a varity of natural phenomena and industrial applications. It is already observed in experiments that the dilute bre 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 bre 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 hydrodynamic translational di usion 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 ow may either die or saturate on a nite amplitude. The character of this long time behaviour is dictated by the wavenumber, the presence or absence of the translational di usivity, rotational di usivity, and the uid 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 ow in the very beginning, due to the combined e ects of the stericdepleted 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 di usivity 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 di erent 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 of the initial perturbations. Descriptors: fi bre suspensions, sedimentation, instability, mixture model, point-particle model
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