Orientation distribution of fibers and rheological property in fiber suspensions flowing in a turbulent boundary layer

A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.

Numerical prediction of the flow property in round turbulent jet of fiber suspension

The equation of probability distribution function for mean fiber orientation,and the equations of Reynolds averaged NavierStokes,turbulence kinetic energy and turbulence dissipation rate with the additional term of the fibers are derived and solved numerically.The effects of fiber concentration and fiber aspect-ratio on the mean velocity profile,turbulent kinetic energy and turbulent viscosity are analyzed.The results show that the mean axial velocity gradient increases near the centerline and decreases near the outside,respectively,as the fiber concentration increases.The mean axial velocity decreases with increasing the fiber concentration at the same radial positions.The centerline mean axial velocity decreases with axial distance,and this phenomenon is more obvious as the fiber concentration increases.The turbulent kinetic energy and turbulent viscosity increase over the jet region with an increasing fiber concentration.The variation tendency of mean axial velocity,turbulence kinetic energy and turbulence viscosity with fiber aspect-ratio is the same as that with fiber concentration.The difference is that the variation with fiber concentration is more obvious than with fiber aspect-ratio.