A New Formula for Predicting the Velocity Distribution in the Turbulent Fiber Suspensions of a Channel Flow
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 are derived and solved numerically to explore the characteristics of fiber suspension flow in a channel. The mathematical model and numerical code are validated by comparing the computational results with the corresponding experimental ones. The effect of Reynolds number, fiber concentration and fiber aspect-ratio on the velocity profile, turbulent intensity, and turbulent dissipation rate is analyzed. The results show that the effect of fibers on turbulent channel flow is equivalent to an additional viscosity, but at this range of fiber concentration, the effect of the presence of fibers was small. The turbulent velocity profiles of fiber suspension become gradually sharper in the central region of channel by increasing the fiber concentration and/or decreasing the Reynolds number. The velocity gradient near the wall decreases gradually as the fiber aspect-ratio increased. The turbulent kinetic energy will increase with increasing Reynolds number, fiber concentration, and fiber aspect-ratio. The turbulent dissipation rate will increase with increasing fiber concentration or decreasing fiber aspect-ratio. Finally, the equation of velocity profile for turbulent fiber suspension channel flow, involving the effect of Reynolds number, fiber concentration, and aspect-ratio, is derived.
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