This study uses novel methods, combining discrete element method (DEM) simulations for packing and computational fluid dynamics (CFD) modeling of fluid flow, to simulate the pressure drop across rigid, randomly packed beds of spheres ranging from 1 to 3 mm in diameter, with porosities between 0.34 and 0.45. This modeling approach enables the combined effect of void fraction and particle size to be studied in more depth than that has been previously possible and is used to give insight into the ability of the well-established Ergun equation to predict the pressure drop behavior. The resulting predictions for pressure drop as a function of superficial velocity were processed to yield coefficients α and β in the Ergun equation and were found to be in keeping with equivalent data in the literature. Although the scatter in α with structural variations was very small, the scatter in β was large (±20%), leading to inaccuracies when used to predict pressure drop data at velocities beyond the Darcy regime. Evaluation of the packed particle structures showed that regions of poor packing, in samples with high porosity and large particle sizes, lead to lower β values. The findings bring strong support to the belief that a generalized model, such as that by Ergun, cannot yield a unique value for β, even for identical spheres.
Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation
