Analysis of the time-averaged gas-solid drag force based on data from transient 3D CFD simulations of fluidized beds

In the present work, a qualitative analysis of the time-averaged gas–solid drag force in gas–solid fluidized beds is carried out. The analysis is based on a large number of transient Eulerian–Eulerian 3D CFD simulations of small bubbling, turbulent and circulating fluidized beds. The obtained results significantly differ from corresponding data previously obtained from 2D simulations, especially at high solid concentrations. This confirms that to accurately model the gas–solid drag force in a steady state 3D simulation, the drag model should not be based on data from transient 2D simulations. In the present work, the average drag force is expressed as the product of the drag force calculated from time-averaged velocities and volume fractions and a correction coefficient. The study shows that even when the third dimension is described in the mesh with only three nodes, the 3D character of the flow is captured in the drag correction coefficient. Thus, a large number of parametric studies could be carried out in a reasonable time frame. In the paper, the parameters affecting the time-averaged drag force are identified and the nature of the effects are analyzed. The analysis shows that solid volume fraction, particle size, solid density, gas viscosity, the slip velocity between gas and solids and the lateral distance to a wall have significant effects on the drag correction coefficient. At high gas densities typical e.g. of pressurized fluidization even the gas density has significant effects. A closure relation for the time-averaged drag force for a wide range of fluidization conditions should include these seven variables as inputs.