(199a) Fluid-Particle Drag in Sheared Particle Configurations

Flows of gas-solid suspensions in large devices are usually analyzed through continuum models that take the form of balance equations for mass, momentum, and fluctuating motion of particle and fluid phases. In the momentum balance equation for the particle phase the dominant forces acting on the particles are usually the gravitational and the fluid-particle drag forces, with the remaining terms such as the divergence of the particle phase stress contributing to a smaller extent in most of the flow domain. As a result, an accurate constitutive model for the fluid-particle drag force is particularly important to predict the flow behavior quantitatively, and has indeed been the subject of a large number of studies in the literature; e.g., see Hill et al. [1], Li & Kuipers [2] and the references cited therein. Quite remarkably, all of the literature studies on this subject have examined (either theoretically or experimentally) the fluid-particle drag force in essentially homogeneous and (nearly) isotropic particle assemblies. However, suspension flows commonly involve spatial inhomogeneities in particle volume fraction and/or anisotropy in the local microstructure (which can arise even in homogeneous systems when the particle phase undergoes deformation). Ten Cate & Sundaresan [3] examined the effect of spatial gradients in particle volume fraction on the drag force and found it to be a small correction, but observed that changes in the radial distribution function for the particles did have measurably large effects on the drag force.

In the present study we have examined the effect of shear in the particle phase on the fluid particle drag force in the Stokes flow regime. When the particle phase undergoes shear, anisotropy develops in the particle microstructure, and fluid flowing through such an assembly experiences a drag force that differs appreciably from that for an isotropic particle assembly (at the same particle volume fraction). The permeability tensor now is distinctly anisotropic, whose extent increases with particle volume fraction. Indeed, this correction to the drag brought about the anisotropy can be as large as or even larger than the contributions to the momentum balance equations arising from the divergence of the particle phase stress. This study exposes the need for constitutive models that account for the changes in the fluid-particle drag force due to the changes in particle microstructure produced by local particle velocity gradients. Such a contribution to the fluid-particle drag may also produce a sizeable change to predicted stability limits of a uniformly fluidized state.

References:

[1] Hill, R., Koch, D., Ladd, A. (2001). The first effects of fluid inertia on flows in ordered and random arrays of spheres. J. Fluid Mech. 448: 243-278.

[2] Li, J., Kuipers, J.A.M. (2003). Gas-particle interactions in dense gas-fluidized beds. Chem. Eng. Sci. 58: 711-718.

[3] Ten Cate, A., Sundaresan, S. (2006). Analysis of the Flow in Inhomogeneous Particle Beds Using the Spatially Averaged Two-Fluid Equations. Int. J. Multiphase Flow, 32: 106-131.