ORIENTATION MODEL FOR PARTICLES IN TURBULENCE

The problem of predicting the orientations of falling nonspherical par ticles has been addressed by the construction of a heuristic model tha t assumes the particles are subject to isotropic turbulence within or below the inertial subrange, that is, the Kolmogorov spectrum of eddie s, depending on the particle dimensions. The rms tilt angle of a spher oidal particle of smalt eccentricity is determined by Langevin-type av eraging over its equation of motion, taking into account the first-ord er 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 stres ses and by assuming the thermal and turbulent fluctuations are uncorre lated, an approximate expression for the variance of an assumed Gaussi an orientation distribution for small tilt angles and small flow Reyno lds numbers is obtained. The expression is then generalized to provide a semiquantitative, nearly Gaussian probability distribution for arbi trary tilt angles, particle aspect ratios, Reynolds numbers. and parti cle sizes relative to the Kolmogorov microscale length for particles t hat can be modeled as spheroids, disks, and cylinders, as well as hexa gonal plates and columns such as ice crystals.