On the influence of the periodic boundary conditions on the drag of random particle arrangements in PR-DNS

Abstract

Particle-resolved direct numerical simulation is an accurate tool for studying aspects of particle-laden flows, allowing, for instance, for the accurate estimation of fluid hydrodynamic forces on particles. While periodic boundary conditions are often used to mimic large suspensions of particles, they can introduce spurious effects if the domain size is not sufficiently large. This work investigates the effect of the domain size on the drag forces experienced by particles in random arrangements. Current practice relies on the diminishing spatial autocorrelation of the fluid velocity fluctuations as a measure to prevent periodicity effects. In this study, the impact on the drag force itself is directly monitored. First, the case of particle pair in Stokes flow is considered at varying inter-particle distances and orientations with respect to the mean flow. This provides the “worst-case scenario” for domain size, i.e. very dilute suspensions and low Reynolds numbers. Second, random arrangements of particles are considered with incrementally expanding periodic domain sizes. The spatial autocorrelation of the fluid velocity fluctuations shows inconsistencies for small domain sizes across different realizations. Additionally, the influence of Reynolds number and particle volume fraction on the correct domain size are investigated separately. The effect of the Reynolds number is found to be small and does not significantly contribute to the effect of domain size. On the other hand, particle volume fraction shows an impactful contribution where lower volume fractions require larger domain sizes to minimize the periodicity effects. Finally, recommendations for the required domain size for PR-DNS are presented.