Effects of heterogeneity on the drag force in random arrays of spheres
Kriebitzsch, S.H.L. and Hoef, M.A. van der and Kuipers, J.A.M. (2008) Effects of heterogeneity on the drag force in random arrays of spheres. In: 6th International Conference on Computational Fluid Dynamics in the Oil & Gas, Metallurgical and Process Industries, CFD 2008, 1012 June 2008, Trondheim, Norway.

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Abstract:  The modelling of the gassolid interaction is a prerequisite in order
to accurately predict fluidized bed behaviour using models such as the Discrete Particle Model (DPM) or the Two Fluid Model (TFM). Currently, the drag force is usually modelled purely based on porosity and slip velocity, which are averaged with respect to the grid size used to solve the model equations. Interfaces at heterogenous structures such as bubbles or free board are not accounted for. As recently pointed out by Xu et al. (2007), subgrid information for the particle position is available in DPM simulations, thus the local porosity is known and can be used when calculating the drag. Direct Numerical Simulation of flow in particulate systems were done using the lattice Boltzmann method. These simulations were carried out with random arrays of spheres which only have a slight degree of heterogeneity and the gassolid interaction force on each particle was measured. First we compared these results, which can be considered as the “true drag force, with the drag force one would predict from a correlation typically used in larger scale models (such as the relation of van der Hoef et al. (2005)). Even for the random arrays, the drag on some individual particles differed considerably (up to 40%) from the predicted drag. Then we evaluate the effectiveness of improved drag models, that use information on local porosity 
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