Abstract
We propose a heuristic model for the transition between collisional and frictional/plastic stresses in the flow
of granular material. Our approach is based on a physically motivated, nonlinear ‘blending’ function that produces a
weighted average of the limiting stresses, depending on the local void fraction in the flow field. Previously published
stress models are utilized to describe the behavior in the collisional (Lun et al., 1984) and quasi-static limits (Schaeffer,
1987 and Syamlal et al., 1993). Sigmoidal and hyperbolic tangent functions are used to mimic the observed smooth yet
rapid transition between the collisional and plastic stress zones. We implement our stress transition model in an opensource
multiphase flow solver, MFIX (Multiphase Flow with Interphase eXchanges, www.mfix.org) and demonstrate its
application to a standard bin discharge problem. The model’s effectiveness is illustrated by comparing computational
predictions to the experimentally derived Beverloo correlation. With the correct choice of function parameters, the
model predicts bin discharge rates within the error margins of the Beverloo correlation and is more accurate than one of
the alternative granular stress models proposed in the literature. Although a second granular stress model in the literature
is also reasonably consistent with the Beverloo correlation, we propose that our alternative blending function is likely to
be more adaptable to situations with more complex solids properties (e.g., ‘sticky’ solids).
