This work numerically studies transient behaviour of particulate flows in a cylindrical‐conical spouted bed in terms of comparative analysis of different models’ predictions. Two approaches were used: a laminar flow model and a turbulent flow model. As a reference case, we consider experimental studies by He et al.,[14,15] where the profiles of vertical particle velocities and the void fraction in the spout and the fountain of a full‐column spout bed were measured. In this work we used the Euler‐Euler unsteady multiphase model with the Syamlal‐O'Brien, Gidaspow, and Wen‐Yu drag models available in commercial CFD software Fluent 14.0. Analysis of results obtained by the use of laminar and turbulent flow models revealed almost identical solid and gas phase velocities and phase fractions within the spouted bed region. We found that the turbulence plays a significant role only in the gas phase above the spouted bed and it does not have any influence on the solid phase. Comparing our simulation results in the form of time‐averaged vertical velocity of the solid phase against experimental data showed acceptable agreement in the spout and very good agreement in the fountain region. Numerical simulations with the Syamlal‐O'Brien drag model gave better agreement with experimental data than results obtained using the Gidaspow and Wen‐Yu drag models. To analyze the transient behaviour of the spouted bed, we use the volume‐averaged particle velocity and gas phase velocity. The analysis of their time histories showed that the start up time is 2–3 s. The developed unsteady regime is reached after 4–5 s. Additionally we studied numerically the influence of different discretization schemes for convective terms on the final results. We found that the use of 1st order upwind scheme gives a steady state solution for both models, laminar and turbulent. Finally, we investigated the influence of the restitution coefficient on the transient characteristics of a cylindrical‐conical spouted bed. A decrease in the value of the restitution coefficient leads to an increase in the period of oscillations of the volume‐averaged velocities of the gas and solid phases.

The main objective of this work is to understand the major peculiarities of the process of clean fracturing fluid being displaced by a flow of particulate suspension (slurry) in a fracture channel. A number of 2D and 3D numerical simulations (based on an Euler‐Euler type model) of slurry flows in channels of complex geometry are carried out. The performance of the model is validated against experimental data by Gillies et al. Euler‐Euler simulations of a laminar slurry flow in a horizontal pipeline showed good agreement between computed and measured particle concentration distributions across a pipe. Numerical studies of slurry flows in 2D and 3D channels show the formation of an M‐shape profile of the solid phase across a channel at the initial fracture section. Our computations demonstrate the rapid growth of a dispersion zone separating a slurry and a clean fluid. It is shown that the dispersion zone is shorter in a tortuous channel than in a straight one. The computations illustrate a reduction in the dispersion zone length with an increase in the fracturing fluid viscosity. The results obtained show the importance of taking into account the previously ignored process of slurry/clean fluid boundary dispersion in prospective hydraulic fracturing simulators.