It has been recognized that, generally, large particles enhance the turbulence intensity, while small particles attenuate the turbulence intensity. However, there has been no consensus on the quantitative criterion for particle-induced turbulence enhancement or attenuation. In the present study, interface-resolved direct numerical simulations of particle-laden turbulent flows in an upward vertical channel are performed with a direct forcing/fictitious domain method to establish a criterion for turbulence enhancement or attenuation. The effects of the particle Reynolds number ( increases with increasing bulk Reynolds number, particle size and particle–fluid density ratio, while increasing with decreasing particle volume fraction, particularly for the channel centre region. Criteria for enhancement or attenuation are provided for the total turbulence intensity in the channel and the turbulence intensity at the channel centre, respectively, and both are shown to agree well with the experimental data in the literature. The reason for the dependence of the critical particle Reynolds number on the other parameters is discussed.

Gas-fluidized beds of flexible fibres, which have been rarely studied before, are investigated in this work using the coupled approach of the discrete element method and computational fluid dynamics. In the present numerical method, gas–fibre interaction is modelled by calculating the interaction force for each constituent element in the fibre, and the composition of the interaction forces on the constituent elements generates a resultant hydrodynamic force and a resultant hydrodynamic torque on the fibre. Pressure drops and fibre orientation results from the present simulations with various fibre aspect ratios are in good agreement with previous experimental and simulation results. Some novel results are obtained for the effects of fibre flexibility. Larger hydrodynamic forces on fibres (before the bed is fluidized) and smaller minimum fluidization velocities (MFVs) are observed for more flexible fibre beds due to the smaller porosities, while smaller hydrodynamic forces are obtained for the more flexible fibres when the beds are fluidized with significant fibre motion. By scaling the superficial gas velocity using the MFVs, the data of pressure drop can collapse onto the Ergun correlation for stiff fibres of various aspect ratios; however, the pressure drop curves deviate from the Ergun correlation for very flexible fibres, due to the significant fibre bed expansion before the MFV is reached. The fibre aspect ratio and flexibility both have an impact on the solids mixing rate, and it is found that the solids mixing rates are essentially determined by the ratio of the superficial gas velocity to MFV.