New equation of turbulent fibre suspensions and its solution and application to the pipe flow

The mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are derived. The successive iteration for calculating the mean orientation distribution of fiber and the mean and fluctuation-correlated quantities of suspension is presented. The equations and their solutions are applied to a turbulent pipe flow of fiber suspension, and a corresponding experiment is performed. It is found that theoretical and experimental results are in good agreement. The obtained results for turbulent pipe flow of fiber suspension show that the flow rate of fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian flow in the absence of fiber suspensions. Fibers play an important role in reducing the flow drag. The amount of reduction in drag augments with the increase in the concentration of the fiber mass. The relative turbulent intensity and Reynolds stress in the fiber suspensions are smaller than those in the Newtonian flow under the same condition, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is directly proportional to the concentration of the fiber mass.