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A numerical method for predicting fiber orientation is presented to explore the flow properties of turbulent fiber suspension flowing through a stock pump impeller. The Fokker-Planck equation is used to describe the distribution of fiber orientation. The effect of flow-fiber coupling is considered by modifying the constitutive mode.The three-dimensional orientation distribution function is formulated and the corresponding equations are solved in terms of second-order and fourth-order orientation tensors. The evolution of fiber orientation, flow velocity and pressure, additional shear stress and normal stress difference are presented. The results show that the evolutions of fiber orientation are different along different streamlines. The velocity and its gradient are large in the concave wall region, while they are very small in the convex wall region. The additional shear stress and normal stress difference are large in the inlet and concave wall regions, and moderate in the mid-region, while they are almost zero in most downstream regions. The non-equilibrium fiber orientation distribution is dominant at the inlet and the concave wall regions. The flow will consume more energy to overcome the additional shearing losses due to fibers at the inlet and the concave wall regions. The change of flow rates has effect on the distribution of additional shear stress and normal stress difference. The flow structure in the inlet and concave wall regions is essential in the resultant rheological properties of the fiber suspension through the stock pump impeller, which will directly affect the flow efficiency of the fiber suspension through the impeller.
A numerical method for predicting fiber orientation is presented to explore the flow properties of turbulent fiber suspension flowing through a stock pump impeller. The Fokker-Planck equation is used to describe the distribution of fiber orientation. The effect of flow-fiber coupling is considered by modifying the constitutive mode. The three-dimensional orientation distribution function is formulated and the corresponding equations are solved in terms of second-order and fourth-order orientation tensors. The evolution of fiber orientation, flow velocity and pressure, additional shear stress and normal stress The results show that the evolutions of fiber orientation are different along different streamlines. The velocity and its gradient are large in the concave wall region, while they are very small in the convex wall region. The additional shear stress and normal stress difference are large in the inlet and concave wall regions, and moderate in the mid-region , while they are almost zero in the most downstream regions. The non-equilibrium fiber orientation distribution is dominant at the inlet and the concave wall regions. The flow will consume more energy to overcome the additional shearing losses due to fibers at the inlet and the concave The change of flow rates has effect on the distribution of additional shear stress and normal stress difference. The flow structure in the inlet and concave wall regions is essential in the resultant rheological properties of the fiber suspension through the stock pump impeller, which will directly affect the flow efficiency of the fiber suspension through the impeller.