Orientation distribution of cylindrical particles suspended in a turbulent pipe flow

A model of turbulent cylindrical particle suspensions is proposed to predict the orientation distribution of particles. The fluctuating equation for the orientation distribution function (ODF) of cylindrical particles is theoretically solved using the method of characteristics. The orientation-correlated terms in the mean equation for the ODF due to the random motion of cylindrical particles are related to the correlations of the mean ODF and the fluid velocity gradient. Thus, the evolution of the mean ODF is described by a modified convection-dispersion equation. The model and modified equation are used to calculate the ODF in a pipe flow numerically. The results compare qualitatively with the experimental data and show that the turbulent dispersion makes cylindrical particles have a broad orientation distribution, while the velocity gradient plays an opposite role. The increase of the particle aspect ratio leads to a less aligned distribution in the vicinity of the axis and a narrower orientation distribution at positions far from the axis.