Stochastic modelling for capturing the behaviour of irregular-shaped non-spherical particles in confined turbulent flows

Abstract

For calculating dispersed particle-ladenflows in confined systems, the well-known Euler/Lagrange approach ismost suitable. Lagrangian tracking of non-spherical particles with certain shapes is mostly performed by addi-tionally solving for the orientation of particles in theflow and using resistance coefficients (i.e. drag, lift andtorque) which depend on this orientation. For that in many cases theoretical results for Stokesflow aroundsuch particles are used. In practical situations where very often irregular shaped non-spherical particles aretransported in aflow, such an approach cannot be adopted since the particles have mostly a statistical distribu-tion of shape and hence it is difficult to define a major and minor axis of the particles. The novel approach devel-oped here is based on a statistical treatment of thefluid forces and moments acting on irregular-shaped particlesas well as the wall collision process in order to mimic their stochastic behaviour. The required probability distri-bution functions (PDF's) for the resistance coefficients were derived by applying direct numerical simulations(DNS) based on the Lattice-Boltzmann method (LBM). The PDF's for the wall normal and parallel restitution ra-tios were developed based on an experimental analysis of the wall collision of irregular-shaped particles usingstereoscopic high-speed imaging. Preliminary Euler/Lagrange calculations applying these statistical modelswere conducted for a horizontal channelflow laden with irregular-shaped particles and compared to measure-ments. The results revealed that the calculation of the particle phase assuming the standard models for sphericalparticles yields completely wrong cross-stream profiles of particle massflux, an under-prediction of the stream-wise particle mean velocity and an over-prediction of the associatedfluctuating component. The stochasticmodels for theflow resistance coefficients and the wall collision process on the other hand provided much betteragreement with the measurements