Numerical prediction of dispersed turbulent liquid–solid flows in vertical pipes

A mathematical model for the simulation of dispersed turbulent liquid–solid flows in vertical pipes is presented. The model is based on the Eulerian–Eulerian approach and solves the averaged mass and momentum conservation equations for both phases, coupled by means of interfacial momentum transfer terms. Its distinctive feature is the modelling of interphase friction and turbulence modulation. In particular, specific source terms which generalize some existing correlations originally developed for gas–solid flows are introduced in the conservation equations for the turbulent kinetic energy of the fluid and its dissipation rate to account for turbulence modulation. By comparison with experimental data available in the literature for different flow conditions, the model revealed that it is capable of reproducing the main features of the flow. Moreover, it proved capable of predicting the effect of particle size on turbulence modulation in liquid–solid flows.