Rheological behavior of fiber suspensions in a turbulent channel flow

Rheological behavior of fiber suspensions in a turbulent channel flow was investigated theoretically and numerically. A model of turbulent fiber suspensions was proposed to predict the orientation distribution of fibers. The fluctuating equation for the orientation distribution function (ODF) of fibers was theoretically solved using the method of characteristics. The self-governed mean equation for orientation distribution function (ODF) was derived by relating the fluctuating ODF and angular velocities-correlated terms to the gradient of mean ODF. Then the ODF of fibers was predicted by numerically solving the mean equation for ODF. Finally the shear stress and first normal stress difference of suspensions were obtained. The results, some of which agree with the available relevant experimental data, show that the orientation distribution of fibers in the vicinity of the center of the flow is relatively broad in turbulent regime, and becomes broader with the increase of Reynolds number. The shear stress of fiber suspensions increases, while the first normal stress difference decreases, from the wall to the center of the flow for varying Reynolds number.