(339u) Fluid-Particle Drag in Inertial Polydisperse Gas-Solid Suspensions

Suspension flows in large devices are generally analyzed using continuum models that treat the particle and fluid phases as interpenetrating continua. These continuum hydrodynamic models consist of balance equations for particle and fluid phase mass, momentum, and energy associated with the fluctuating motion. In the momentum balance equation for the particle phase, the dominant forces acting on the particles are those due to gravity and fluid-particle drag; as a result, a significant amount of research has been performed in the literature, with the aim of developing constitutive relations for the fluid-particle drag, e.g. see Koch et al. [1] and references cited therein. Most of the research performed to date has been devoted to developing constitutive models for monodisperse suspensions (i.e., particles of the same size and/or density). However, polydispersity is inevitable in industrial scale devices, and it can alter the flow characteristics appreciably [2]. The effect of polydispersity on the fluid-particle drag force in fixed beds has also been studied extensively in the literature; for example, see recent publications by van der Hoef et al. [3] and Beetstra et al. [4], who employed a computational approach to formulating constitutive models. In polydisperse suspensions, particles of different sizes (and/or densities) will, in general, have different local average velocities and this relative velocity between particles of different types can impact the magnitude and direction of the net fluid-particle drag force. More general constitutive models for the gas-particle drag force that permit relative motion (in a local average sense) between particles of different types, valid in the Stokes flow limit, were presented recently by Yin & Sundaresan [5, 6].

In this study we extend the fluid-particle drag relation presented by Yin & Sundaresan by taking into account the effect of moderate fluid inertia. Towards this end, we have performed simulations of fluid flow through bidisperse particle assemblies in periodic domains using the lattice Boltzmann simulation method [7], which has been used in a number of previous studies [1, 3-6], to obtain computational data for formulating constitutive models for the drag force. We find that a fluid-particle drag force model that combines the bidisperse suspension drag law in the Stokes flow limit proposed by Yin & Sundaresan [6] and the moderate inertia correction for polydisperse fixed bed drag proposed by Beetstra et al. [4] adequately captures our simulation data.

In this poster, we will present the polydisperse fluid-particle drag force model that allows for the presence of moderate fluid inertia and relative motion (in a local average sense) between particles of different types, and discuss the relative importance of the fluid-mediated particle-particle interactions and that resulting from direct particle-particle collisions at different levels of fluid inertia.

References:

[1] Koch, DL & Hill, R. (2001). Inertial effects in suspension and porous-media flows. Annu. Rev. Fluid Mech., 33: 619-647.

[2] Hoffman, AC, Janssen, LPBM & Prins, J. (1993). Particle segregation in fluidized binary mixtures. Chem. Eng. Sci., 48: 1583-1592.

[3] van der Hoef, MA, Beetstra, R & Kuipers, JAM. (2005). Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for permeability. J. Fluid Mech., 528: 233-254.

[4] Beetstra, R, van der Hoef, MA & Kuipers JAM. (2007). Drag Force of Intermediate Reynolds Number Flow Past Mono- and Bidisperse Arrays of Spheres. AIChE J., 53: 489-501.

[5] Yin, X & Sundaresan, S. (2009). Drag Law for Bidisperse Gas-Solid Suspensions Containing Equally Sized Spheres. Ind. Eng. Chem. Res., 48: 227-241

[6] Yin, X & Sundaresan, S. (2009). Fluid-particle drag in low-Reynolds-number polydipserse gas-solid suspensions. AIChE J., (in press)

[7] Ladd, A.J.C. & Verberg, R. (2001). Lattice-Boltzmann simulation of particle-fluid suspensions. J. Stat. Phys., 104: 1191-1251.