Drag force modelling in dilute to dense particle-laden flows with mono-disperse or binary mixture of solid particles
Résumé
Fluid-particle momentum transfer modelling is a key issue for the simulation of gas-solid fluidized beds. In the literature, many empirical correlations can be found for the prediction of the drag force but these correlations are generally not satisfactory for all the flow conditions found in fluidized bed: dilute and dense regime, low and high particle Reynolds number values, mono- or polydisperse solid mixture. Up to now, in dense particulate flows, the validation of such correlations were performed only by comparison with experiments using mean pressure drop, fluidization or settling velocity measurements and analytical solutions in some limit cases (Stokes flow). Nowadays, the development of particle resolved numerical techniques, like Lattice Boltzmann Method (LBM), allows to perform Direct Numerical Simulation (DNS) of the flow across dilute and dense particle arrays. Such simulations allow to compute directly the forces acting on the particles which may be used to validate or develop drag force correlations. In the present paper, we show that the simple drag correlation proposed by Gobin et al. (2003), and already used extensively for circulating and dense fluidized bed simulation, is in very good agreement with the particle-resolved immersed boundary-method results of Tenneti et al.(2011) and with the boddy-fitted DNS results of Massol. An extension of the correlation is also proposed for poly-disperse mixture based on the LBM results of Beetstra et al. (2007).
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