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

摘要

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