Fluid-particle interaction force for polydisperse systems from lattice boltzmann simulations

Gas-solid fluidized beds are almost always polydisperse in industrial application. However, to describe the fluid-particle interaction force in models for large-scale gas-solid flow, relations are used which have been derived for monodisperse system, for which ad-hoc modifications are made to account for polydispersity. Recently it was shown, on the basis of detailed lattice Boltzmann simulations, that for bidisperse systems these modifications predict a drag force which can be factors different from the true drag force. In this work fluid-particle interaction forces for polydisperse system are studied by means of lattice Boltzmann simulation, using a grid that is typically an order of magnitude smaller than the sphere diameter. Two different lognormal size distributions are considered for this study. The systems consist of polydisperse random arrays of spheres in the diameter range of 8-24 grid spacing and 8-40 grid spacing, a solid volume fraction of 0.5 and 0.3 and Reynolds number 0.1 to 500. The data confirms the observations made for bidisperse systems, namely that an extra correction factor for the drag force is required to adequately capture the effect of polydispersity. It was found that the correction factor derived by van der Hoef et al (J. Fluid Mech. 528 (2005) 233) on the basis of bidisperse simulation data, applies also to general polydisperse systems.