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

Abstract

For calculating dispersed particle-laden flows in confined systems, the well-known Euler/Lagrange approach is most suitable. Lagrangian tracking of non-spherical particles with certain shapes is mostly performed by additionally solving for the orientation of particles in the flow and using resistance coefficients (i.e. drag, lift and torque) which depend on this orientation. For that in many cases theoretical results for Stokes flow around such particles are used. In practical situations where very often irregular shaped non-spherical particles are transported in a flow, such an approach cannot be adopted since the particles have mostly a statistical distribution of shape and hence it is difficult to define a major and minor axis of the particles. The novel approach developed here is based on a statistical treatment of the fluid forces and moments acting on irregular-shaped particles as well as the wall collision process in order to mimic their stochastic behaviour. The required probability distribution 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 ratios were developed based on an experimental analysis of the wall collision of irregular-shaped particles using stereoscopic high-speed imaging. Preliminary Euler/Lagrange calculations applying these statistical models were conducted for a horizontal channel flow laden with irregular-shaped particles and compared to measurements. The results revealed that the calculation of the particle phase assuming the standard models for spherical particles yields completely wrong cross-stream profiles of particle mass flux, an under-prediction of the stream-wise particle mean velocity and an over-prediction of the associated fluctuating component. The stochastic models for the flow resistance coefficients and the wall collision process on the other hand provided much better agreement with the measurements.