A successive iteration method on predicting properties of turbulent fiber suspensions and its application to pipe flows

Abstract

The modified Reynolds-averaged equation of motion for the turbulent fiber suspensions and the equation of probability distribution function for mean fiber orientation are derived. A successive iteration method is used for solving these equations. The method is applied to a turbulent pipe flow, and the probability distribution for mean fiber orientation, the streamwise mean velocity, the root mean square (rms) velocity fluctuations and the Reynolds stress are calculated. A satisfactory agreement between numerical and experimental results indicates that the method is reasonable and reliable, and can be methodologically applied to any incompressible turbulent flows of fiber suspensions. The results on the pipe flows show that most fibers orient along the flow. The rms radial velocity fluctuations are smaller than the rms streamwise velocity fluctuations. The maximum of rms velocity fluctuation appears in the near wall region. As the fiber mass concentration increases, the steepness of mean velocity profile increases, while the rms velocity fluctuation and the Reynolds stress decrease. The fibers suppress the turbulence and result in a reduction in Reynolds stress, and the effect of suppression and the amount of reduction are directly proportional to the fiber mass concentrations. The Reynolds number has less effect on the velocity profile. As the Reynolds number increases, the mean velocity profile becomes blunter, and the rms velocity fluctuations and the Reynolds stress increase. The effect of fiber aspect ratio on the mean velocity is more obvious than that of Reynolds number. As the fiber aspect ratio decreases, the mean velocity profile becomes blunter, and the rms velocity fluctuations and Reynolds stress decrease.