Abstract

 

The results from hard-particle, discrete element simulations of two- and three- dimensional, dilute granular flows past an immersed sphere and cylinder are presented. Simulation measurements of the drag force, F_d, are expressed in terms of a drag coefficient, for 2-D, and  for 3-D, where r is the particle density,   is the upstream solid fraction,  U is the upstream instantaneous velocity,  and D and d are the sphere and particle diameters, respectively.  The sphere's drag coefficient is a function of the flow Knudsen number,

 and .