(388ab) Lattice Boltzmann Method (LBM) Simulations of Gas-Solid Flows Containing Non-Spherical Particles

A good understanding of particle-fluid interactions is crucial to predict better the dynamics of various industrial processes and natural phenomena, e.g. chemical reactors, the transport of pollutants in the atmosphere or the transport of sediments in rivers. In those systems, the dynamics of particles are highly complex due to (і) particle-particle, (іі) particle-fluid and (ііі) particle-wall interactions.

Currently the drag force correlations of Ergun or Wen &Yu are commonly used. However, these correlations are often applied for conditions in which their validity is questionable. Direct numerical simulations using e.g. the lattice Boltzmann method would allow us to measure fluid-particle interactions and, thus, formulate accurately drag force correlations.

Koch (Koch and Sangani 1999; Koch and Hill 2001; Koch and Ladd 2001a, b) was the first to develop a drag force correlation based on lattice Boltzmann simulations. Van der Hoef and Beetstra (van der Hoef 2004; Beetstra 2007) extended the work of Koch et. al. establishing a new drag force correlation for mono- and bidisperse arrays of spheres.  In these simulations, the flow field around a random array of spheres was computed using a lattice Boltzmann method with a grid sufficiently small to model the detailed flow around the spheres. The drag force correlations derived from lattice Boltzmann simulations showed a better agreement with experimental measurements than the traditional Ergun and Wen &Yu correlations.

Numerical simulations of gas-fluidized beds have been restricted mostly to spherical particles due to a lack of drag force correlations for non-spherical particle assemblies. Indeed, even for a single non-spherical particle only limited work has been reported. For example, Holzer (2007) using lattice Boltzmann simulations proposed a drag force correlation for a single non-spherical particle as a function of particle orientation and Reynolds number. However, these correlations cannot be applied directly to simulate gas-fluidized beds. Here, we develop a drag force correlation for non-spherical particles. The effect of particle shape on the drag force was studied in detailed. The new drag force correlation derived here is suitable for Euler-Euler and Euler-Lagrangian simulations of gas-fluidized beds.

References

Koch, D. L., Sangani, A. S. 1999 Particle pressure and marginal stability limits for homogeneous monodisperse gas fluidized bed: kinetic theory and numerical simulations. J. Fluid Mech. 400, 229

Koch, D. L., Hill, R. j. 2001 Inertial effects in suspension and porous media flow. Annu. Rev. Fluid Mech. 33, 619

Hill, R. J., Koch, D. L., Ladd, A. J. C. 2001a The first effects of fluid inertia on flows in orderd and random arrays of spheres. J. Fluid Mech. 448, 213

Hill, R. J., Koch, D. L., Ladd, A. J. C. 2001b Moderate-Reynolds –number flows in order and random arrays of spheres. J. Fluid Mech. 448, 243

Van der Hoef, M. A., Beetstra, R., Kuipers, J. A. M. 2004 Lattice-Boltzmann simulations of low Reynolds number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233

Beetstra, R., van der Hoef, M. A., Kuipers, J. A. M. 2007 Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres. J. AIChE. 53,489

Holzer, A., Sommerfeld, M. 2007 New simple correlation formula for the drag coefficient of non-spherical particles. Powder Technology, 184, 361