Pairwise interaction extended point-particle model for a random array of monodisperse spheres

Abstract

This study introduces a new point-particle force model that attempts to account for the hydrodynamic influence of the neighbouring particles in an Eulerian–Lagrangian simulation. In previous point-particle models the force on a particle depends only on Reynolds number and mean volume fraction. Thus, as long as the mean local volume fraction is the same, the force on different particles will be estimated to be the same, even though the precise arrangement of neighbours can be vastly different. From direct numerical simulation (DNS) it has been observed that in a random arrangement of spheres that were distributed with uniform probability, the particle-to-particle variation in force can be as large as the mean drag. Since the Reynolds number and mean volume fraction of all the particles within the array are the same, the standard models fail to account for the significant particle-to-particle force variation within the random array. Here, we develop a model which can compute the drag and lateral forces on each particle by accounting for the precise location of a few surrounding neighbours. A pairwise interaction is assumed where the perturbation flow induced by each neighbour is considered separately, then the effects of all neighbours are linearly superposed to obtain the total perturbation. Faxén correction is used to quantify the force perturbation due to the presence of the neighbours. The single neighbour perturbations are mapped in the vicinity of a reference sphere and stored as libraries. We test the pairwise interaction extended point-particle (PIEP) model for random arrays at two different volume fractions of $\unicode[STIX]{x1D719}=0.1$ and 0.21 and Reynolds numbers in the range $16.5\leqslant Re\leqslant 170$. The PIEP model predictions are compared against drag and lift forces obtained from the fully resolved DNS simulations performed using the immersed boundary method. Although not perfect, we observe the PIEP model prediction to correlate much better with the DNS results than the classical mean drag model prediction.