An Exact Method for Determining Local Solid Fractions in Discrete Element Method Simulations

A novel solid fraction algorithm is presented which accounts for the partial volume of a sphere straddling cuboidal bin boundaries. The algorithm accounts for spheres intersecting a single plane (face), two perpendicular planes (edge), or three perpendicular planes (corner). Comparisons are made against the more common algorithm in which the solid fraction is determined by assigning the sphere's total volume to the bin in which the sphere's center of volume (COV) is located. Bin size-to-sphere diameter ratios >30 must be used to give errors <5% when using the traditional method when applied to simple cubic (SC) and hexagonal packing assemblies. Bin size-to-sphere diameter ratios larger than five are required for random sphere packings. Although time averaged solid fraction measurements are similar using either the exact or COV solid fraction schemes, the scatter in the COV method is much larger than for the exact method. (C) 2010 American Institute of Chemical Engineers AIChE J, 56: 3036-3048, 2010