On Fibre Suspension Flow Modelling: Mechanical Fibre Flocculation and Fibre Orientation

Marko Hyensjˆ 2005 Department of Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden.

Abstract In this work the main target is to study numerically the mechanical flocculation and fibre orientation for a cellulose fibre suspension. The aim is specially to develop models for turbulent flows in complex geometries, i.e. typical to be found in paper machine equipment. Furthermore the aim is to study the dilute consistency regime, i.e. <1%, which is expected in papermaking. Different mechanical flocculation models for turbulent one phase flow is tested for various geometries, i.e. a sudden pipe expansion and a planar contraction. The sudden pipe expansion is studied for various flow rates and with fixed step size and fibre properties. For the planar contraction two flocculation models in literature are evaluated. Various parameters such flow rate, fibre properties, inlet turbulence quantities are explored. The fibre floccualtion model captures some general phenomena known from experiments, in particular the prediction of a minimum in flocculation intensity after the step of a sudden pipe expansion, and the subsequent re-flocculation process. Varying the fibre properties, i.e. fibre length and diameter, different behaviors of the flocculation intensity evolution in a planar contraction is predicted for typical headbox flows. Longer fibres are activated easier and from an equilibrium state at the inlet the flocculation intensity increases throughout the contraction. A shorter fibre such as birch will predict the opposite. In addition both long and short fibres will give an increase in flocculation intensity starting from a non-equilibrium state at low intensity. This trend is supported in experimental result from the literature. An Eulerian propability density function is determined by solving a convectiondispersion equation describing the evolution of fibre orientation in a combined extensional and shear flow. This numerical approach is used to evaluate the effect of turbulence generating vanes and wall boundary layers on fibre orientation distribution in a planar contraction. The boundary layer will for both in the plane of paper and in the plane of contraction wider the fibre orientation distributions, i.e the fibres will be less oriented. For the outlet profile of the contraction the fibre orientation distribution will be more effected by the blunt vane tip than the tapered vane tip. The model is validated with experimental results in literature and a good qualitative agreement was achieved.

Descriptors: fibre suspension, fibre flocculation, fibre orientation, flow contraction, pipe expansion, headbox, turbulent flow, anisotropy