Study of the Rotational Diffusivity Coefficient of Fibres in Planar Contracting Flows with Varying Turbulence levels

Authors: Hyensjö, null, Dahlkild, A. A.
Document Type: Article
Pubstate: Published
Journal: International Journal of Multi-Phase Flow
Volume: Vol. 34, Issue 9   894-903
Year: 2008


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, Lf /n >25, compared to the Kolmogorov scale and in the limit of large Rek 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.