Pressure loss and wall shear stress in flow through confined sphere packings

Randomly structured, confined sphere packings with different porosities are generated and the fluid flow within the porous structure is calculated. These locally resolved fluid flow data – instead of integral parameters – are used to investigate the origins of the pressure loss within a packing. First, an analysis and comparison of averaged local velocities is performed to compare the similarity of the simulation approach with empirical relations by means of the void fraction and the velocity distributions. Next, the pressure losses due to mean values of the simulated, locally resolved wall shear stresses are calculated, and these findings are smaller than the results from the integral approach of Kozeny and Carman. This indicates that the pressure drop, even at low Reynolds numbers, is not solely caused by the wall shear stress; the simulated overall pressure drops exceed the Ergun approach, an effect which is caused by the bounded flow within a capillary. To relate the pressure loss due to these secondary pressure losses, the tortuosity of the fluid flow in the porous structure is introduced and this parameter improves the performance of the pressure drop equation.

► Locally resolved velocity fields of sphere packings in capillaries are calculated.
► The radial velocity distribution correlates with experimental findings.
► The averaged wall shear stress suggests the use of an extended volumetric surface.
► The secondary pressure loss is caused by the tortous flow through the packings.
► Comparisons with the Ergun equation confirms the introduction of a tortuosity parameter.