Hydrodynamic force and torque fluctuations in a random array of polydisperse stationary spheres

Abstract: We report data on the fluctuations of hydrodynamic force and torque exerted on polydisperse stationary spheres randomly distributed in a cubic tri-periodic box. We generate our data with an accurate Particle-Resolved/Direct Numerical Simulation (PR-DNS) method that relies on an Immersed Boundary/lattice Boltzmann method implemented on a Cartesian octree grid. The local grid refinement capability offered by the octree grid enables us to properly resolve the flow dynamics even around the smallest stationary spheres in the system in the case of a wide sphere diameter distribution. We verify that our data are indeed accurate and reliable through a thorough comparison with results produced by other numerical methods and with data published in the literature. We evaluate the accuracy and limitations of various average drag models on different levels of polydispersity. We consider two Reynolds numbers $Re=1$ and $Re=100$ representative of low and moderate inertia. We analyze results in terms of hydrodynamic force and torque fluctuations around the average value and relate these fluctuations to the flow disturbances created by the neighboring particles, i.e., the local microstructure. Finally, we discuss the implications of the presented results on the extension of hydrodynamic force and torque models recently proposed in the literature that take advantage of the local microstructure to predict fluctuations in the case of arrays of monodisperse stationary spheres to the case of arrays of polydisperse stationary spheres.