(398h) Drag Force Correlation for Assemblies of Non-Spherical Particles in Gas-Fluidized Bed

Gas-solid systems are of significant industrial importance and are the basis of various reactor concepts, e.g. gas-fluidized beds or rotary kilns. However, with regards to numerical modeling of those systems, very little is known about the force that exerts on the individual particles, when fluid flows past an assembly of particles, the drag force. Thus, a good understanding of particle-fluid interactions is essential to predict more accurately the dynamics of these systems.

Using a multi-scale modeling approach, the closure relationship which describes the effective particle-particle interaction can be obtained from discrete particle simulations, whereas the closure relationship describing the effective fluid-particle interaction can be obtained from empirical relations or direct numerical simulation (DNS). Currently, the drag force correlations of Ergun (1952) or Wen &Yu (1966) 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 (LBM) allows us to measure fluid-particle interactions and, thus, formulate accurately drag force correlations.

Using LBM, Koch (Koch and Hill, 2001) developed a drag force correlation for an array of spheres. Van der Hoef and Beetstra (van der Hoef et al., 2004; Beetstra et al., 2007) extended the work of Koch and Hill (2001) establishing a new drag force correlation for mono- and bi-disperse arrays of 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.

However, due to a lack of drag force correlations for assemblies of non-spherical particles, numerical simulations of gas-fluidized beds have been restricted mostly to beds containing spherical particles. Indeed, even for single non-spherical particles comparatively little work has been reported. For example, Tran-Cong et al. (2004) measured the drag force coefficients for isolated non-spherical particles constructed from several identical spheres. On the other hand, Hölzer et al. (2007, 2009), using lattice Boltzmann simulations, correlated the drag force acting on single non-spherical particles with particle orientation and Reynolds number. However, these correlations cannot be applied directly to simulate gas-fluidized beds since they do not account for the influence of the solids volume fraction on the drag coefficient. Here we report the development of a drag force correlation for non-spherical particle assemblies constructed from identical spheres using LBM. The effect of particle shape and Reynolds numbers on the drag force is studied in detailed. The new drag force correlation developed here is suitable for Euler-Euler and Euler-Lagrangian simulations of gas-fluidized beds comprised of non-spherical particles.

Reference

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[2] C.Y. Wen and Y.H. Yu. Mechanics of fluidization. Chem. Eng. Progr. Symp. Series, 62:100-111, 1956.

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

[4] M.A. Van der Hoef, R. Beetstra, J.A.M. Kuipers. Lattice-Boltzmann simulations of low Reynolds number flow past mono- and bi-disperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech., 528: 233-54, 2004.

[5] R. Beetstra, M.A. Van der Hoef, J.A.M. Kuipers. Drag force of intermediate Reynolds number flow past mono- and bi-disperse arrays of spheres. AIChE J., 53: 489-501, 2007.

[6] S. Tran-Cong, M. Gay, E.E. Michaelides. Drag coefficients of irregularly shaped particles. Powder Technol., 139: 21-32, 2004.

[7] A. Hölzer, M. Sommerfeld. New simple correlation formula for the  drag coefficient of non-spherical particles. Powder Technol., 184: 361-365, 2007.

[8] A. Hölzer, M. Sommerfeld. Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles. Comput. Fluids, 38: 572-589, 2009.