A computational method for simulating dispersed two-phase flows using the PDF approach

Abstract

The thesis presents a Probability Density Function (PDF)-derived Eulerian/Eulerian model for the prediction of dispersed two-phase (solid/gas) flows. Continuum equations for the dispersed phase are formulated from the Kinetic Model (KM) PDF transport equations. The Kinetic stresses of the dispersed phase are determined from an algebraic stress model (ASM) together with a KM-based transport equation for the fluctuating kinetic energy. The continuum equations for the continuous phase are assumed to be the same as those in the Eulerian two-fluid model except for the interfacial momentum and energy transfer terms. Closures for these terms are derived from the PDF KM and mirror their counterparts in the dispersed phase equations. Also, the carrier phase turbulence is modelled by the standard k-ε model. These transport equations are solved using the numerical framework of an existing two-fluid approach. Furthermore, the current two-fluid model practice of applying wall functions to impose boundary conditions is adapted for application to the particulate phase. Such wall functions are calculated from the PDF KM itself. In this approach, the PDF equations are pre-integrated using the fully developed flow assumption along the wall to relate wall fluxes to values of the relevant variables in the interior of the flow. Such integration is utilised to create a wall functions database for a range of mean flow conditions. The model is validated against a range of both unbounded and bounded flow cases. Comparisons are made with experimental data as well as the results of other computational methods. It was found that the proposed model performs very well in capturing particulate behaviour and improves, in certain aspects, on the performance of traditional two-fluid models while retaining the practicality of the latter model for industrial applications. In particular, a reasonable capture of the particulate dispersion was observed within jet flows. Improvements were also seen in the prediction of mass flux distribution in shear layers and an accurate capture of near-wall mass distributions in bounded flows.