Force variation within arrays of monodisperse spherical particles

This study presents a direct numerical simulation analysis of the force distribution within a cluster of monodisperse spherical particles. A direct forcing immersed boundary method is used to calculate the forces on individual particles for a volume fraction range of $0.11\le \varphi \le 0.44$ and a Reynolds number range of $1.47\le \mathrm{Re}\le 636$. The hydrodynamic streamwise force is shown to have a normal distribution with a standard deviation ratio to the mean drag that decreases with increasing volume fraction and ranges between 17% and 26%. The lift forces also follow a normal distribution that has a significant standard deviation to mean drag ratio of around 14.5%, which does not vary significantly with the Reynolds number and volume fraction. A model is introduced that adds the identified normal distribution of the forces to the quasisteady force used in point-particle models. A nonisotropic method of defining spatial parameters is presented. It highlights the contribution of each parameter to the variation of the forces on each particle. The results show that the drag is influenced by the closest four to eight neighboring spheres. The drag force is highly dependent on the streamwise distances of the spheres located upstream. For low volume fractions and Reynolds number, the lateral distances of the spheres located downstream also have a significant contribution to those variations. The results also show that the lateral force variation is mostly dictated by the lateral distance of one to two spheres located upstream of each sphere.