A hybrid continuum/PDF model for the prediction of dispersed particulate flow

The paper presents a hybrid continuum-PDF model for the prediction of dispersed two-phase (solid/gas) flows within confined geometries. Based upon the framework of the two-fluid model, the dispersed phase continuum transport equations are replaced by similar ones derived from the Kinetic Model (KM) PDF transport equations. Closures for the kinetic stresses of the dispersed phase comprise an algebraic stress model (ASM) and a transport equation for the turbulent kinetic energy (kd) – both of which have also been derived from the KM PDF transport equation. The dispersed phase wall boundary conditions are implemented in the same manner as the “wall functions” approach for the numerical solution of the carrier phase continuum equations; however the wall fluxes are calculated from the direct solution of the KM PDF – which has been pre-integrated for a range of bulk flow conditions to produce a database for wall fluxes that are used to set appropriate values at every point along the walls. Validation is made by comparisons against experimental data for a round jet and a confined planar jet. The predictions are in good overall agreement with measurements in both cases. The proposed ASM-kd model shows particularly promising results for the jet flow case, with a large improvement on the results of the standard two-fluid models. However, the planar jet case showed that due to the perfectly reflecting wall condition assumptions used in the production of the wall fluxes database, the particulate mean axial velocity is under-predicted.