The motion of fibres in turbulent flow, stochastic simulation of isotropic homogeneous turbulence

The state of fibres suspended in a turbulent fluid is described in terms of a probability distribution function of fibre orientation and position throughout the suspending fluid. The evolution of the fibre's probability distribution function is governed by a convection–dispersion equation, where the randomizing effect of the turbulence is modelled by rotational and translational dispersion coefficients. To estimate these coefficients a numerical simulation of fibres moving in a turbulent fluid was developed. The trajectory of an ensemble of inertialess, rigid, thin, free-draining fibres was calculated through a stochastic model of homogeneous, isotropic turbulence. The results of the simulation were compared with analytical estimates and were found to provide reasonable agreement over a wide range of fibre length. However, the simulation showed that the Lagrangian integral time scale for rotation was significantly smaller than for translation and the ratio of rotational to translational Lagrangian time scales was smaller than the ratio of Eulerian time scales. The simulation also showed that the Lagrangian velocity correlation increased as fibre length increased and that the temporal correlations approached the analytical estimates of the Eulerian correlations in the limit of long fibres.