UBC Theses and Dissertations
The effects of anisotropic turbulence on fibre motion Holt, Kyle
Fibre orientation and concentration distributions in a turbulent suspension are typically modeled by the Fokker-Planck equation and dispersion coefficients that relate the fluid turbulence properties to the fibre length, assuming an infinitely thin, and inertialess fibre. These predictions are used in a wide variety of engineering problems, notably the forming of paper. There is substantial literature examining the application of the Fokker-Planck equation for isotropic turbulence, however, there are few studies that examine the effect of turbulence anisotropy on fibre translational and rotational dispersion. In order to provide better estimates of fibre orientation and concentration distributions in an anisotropic turbulent suspension, the relationship between turbulence and fibres needs to be better understood. This thesis develops a stochastic model which can be used to determine the orientational and translational dispersion coefficients. The fluid model is based on the Kraichnan turbulence fluid model  and the fibres are represented by rigid, inertialess infinitely thin particles assumed to be in a dilute suspension. The turbulence is made axisymmetric by utilizing the time dependent wavevector relation from Rapid Distortion Theory . This enables the model to simulate the physical effects of eddy distortion by a contraction. A range of fibre lengths and contraction ratios were modeled, and it was found that the translational dispersion coefficient increases in magnitude with contraction ratio and decreases with fibre length while the rotational dispersion coefficient decreases with both contraction ratio and fibre length. A constant was found relating the isotropic and anisotropic translational dispersion coefficients, based on contraction ratio. The simulation showed that the integral time scale for translation increased for short fibres and decreased for long fibres as contraction ratio increased for both directions. The integral time scale for rotation decreased for small fibres and increased to a maximum before decreasing for long fibres as contraction ratio increased for both directions. It was shown that fibre orientation tended to the radial orientation preferentially as contraction ratio increased but spent more time in the streamwise orientation as fibre length increased. These findings will allow for improved estimates to be made for anisotropic dispersion coefficients.
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