Abstract
In loose or moderately-dense particle mixtures, the contact forces between particles due to successive collisions create average volumetric solid-solid drag force between different granular phases (of different particle sizes). The derivation of the mathematical formula for this drag force is based on the homogeneity of mixture within the calculational control volume. This assumption especially fails when the size ratio of particles grows to a large value of 10 or greater. The size-driven inhomogeneity is responsible to the deviation of intergranular force from the continuum formula. In this paper, we have implemented discrete element method (DEM) simulations to obtain the volumetric mean force exchanged between the granular phases with the size ratios greater than 10. First, the force is calculated directly from DEM averaged over a proper time window. Second, the continuum formula is applied to calculate the drag forces using the DEM quantities. We have shown the two volumetric forces are in good agreement as long as the homogeneity condition is maintained. However, the relative motion of larger particles in a cloud of finer particles imposes the inhomogeneous distribution of finer particles around the larger ones. We have presented correction factors to the volumetric force from continuum formula.
Highlights
The solid-solid drag force plays a key role in the hydrodynamics of gas-solid systems such as fluidized beds [1]
The large size ratio is associated with the presence of big particles in a cloud of small particles, which could normally result in the inhomogeneous distribution of cloud particles around any big particle
Note that the force obtained from Eq (1) is a volumetric measure, which raises an important question on how it can be linked to any continuum formulation such as Eq (2)
Summary
The solid-solid drag force plays a key role in the hydrodynamics of gas-solid systems such as fluidized beds [1]. In computer simulations of gas-solid systems using Eulerian approach, the solid-solid drag force is represented by a continuum formula known as the Syamlal equation [2] This formula is derived based on the assumption of homogeneous mixtures of granular phases. It is assumed that the distribution of particles within any local volume remains uniform This assumption could be precise enough when there is monodisperse packing, any large size ratio between the granular phases can violate the homogeneity assumption used in the Syamlal equation. The distribution of solid volume fraction (of small particles) and the collision forces on the big particle would be dependent of the relative motion of the big particle with respect to the particle cloud Such anisotropy in the distribution of collisional forces causes the deviation of mean collisional forces from the predicted values by the Syamlal equation. The focus of this work is to present a correction method of the relevant factors such as the solid volume fraction in terms of the direction of the relative motion of the two granular phases, which lead to a corrected value of the solid-solid drag force
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