Orientation Model for Particles in Turbulence

Abstract

The problem of predicting the orientations of falling nonspherical particles has been addressed by the construction of a heuristic model that assumes the particles are subject to isotropic turbulence within or below the inertial subrange, that is, the Kolmogorov spectrum of eddies, depending on the particle dimensions. The rms tilt angle of a spheroidal particle of small eccentricity is determined by Langevin-type averaging over its equation of motion, taking into account the first-order restoring torque that arises when the stable fall mode is perturbed by either thermal or turbulent fluctuations. By invoking dimensional constraints concerning the nature of the main flow and turbulent stresses and by assuming the thermal and turbulent fluctuations are uncorrelated, an approximate expression for the variance of an assumed Gaussian orientation distribution for small tilt angles and small flow Reynolds numbers is obtained. The expression is then generalized to provide a semiquantitative, nearly Gaussian probability distribution for arbitrary tilt angles, particle aspect ratios, Reynolds numbers, and particle sizes relative to the Kolmogorov microscale length for particles that can be modeled as spheroids, disks, and cylinders, as well as hexagonal plug and columns such as ice crystals.