A New Expression for the Velocity Profile in the Turbulent Pipe Flows of Fiber Suspension
The equation of Reynolds averaged Navier-Stokes with the term of additional stress resulted from fibers and the equation of probability distribution function for mean fiber orientation with the second- and fourth-order orientation tensor of the fiber were derived and solved to explore the characteristics of turbulent fiber suspension in the turbulent pipe flows of fiber suspension. The effect of Reynolds number, fiber concentration and fiber aspect-ratio on the mean velocity were presented and analyzed. It was found that the velocity profile of fiber suspension becomes sharper with decreasing the flow rate and/or increasing the fiber concentration, which agrees with the corresponding experimental ones. The velocity profile becomes steeper as fiber aspect-ratio increases. Fibers at this range of concentration and scales play a role in the increase of viscosity. Finally, the prediction formula of velocity profile involving the effect of Reynolds number, fiber concentration, and aspect-ratio for the turbulent pipe flows of fiber suspension was derived.
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