I've noticed a confusing difference between the theory manual for the newest version of Fluent (18.2) and previous papers on/versions of Fluent regarding volume fraction in the governing equations for granular flow. The new theory manual seems to use volume fraction squared in all of the granular viscosity terms (shear, bulk, frictional and collisional), whereas the old manual uses a linear dependence (i.e. raised to the power of one). I've attached an example below:
From page 550 of the 18.2 ANSYS Fluent Theory Guide (see double appearance of the alpha_s term):
From Fluent 6 and Wachem paper "Derivation, Simulation and Validation of a Cohesive Particle Flow CFD Model" (first line of equation 28 below, epsilon is volume fraction here):
This alpha_s versus alpha_s^2 difference exists for all terms in the "new" expressions for granular viscosity. Am I missing something?