Laminar flow past an infinite planar array of fixed particles: point-particle approximation, Oseen equations and resolved simulations

In the point-particle model of disperse multiphase flow, the particles, assumed to be very small compared with all the scales of the flow, are represented by singular forces acting on the fluid. The hydrodynamic forces are found from standard correlations by interpolating the velocity field from the grid nodes to the particle positions, with the implicit assumption that the computational cells are much larger than the particles. It is argued here that this model has similarities with the Oseen linearization of the Navier-Stokes equation, the most important one being that, in the Oseen context, the particles are also treated, to leading order, as singularities. For this and other reasons addressed in the paper, the Oseen equations can be used as proxies for the point-particle model and the comparison of their solutions with particle-resolved simulations, both of which are presented in this paper, can shed light on the strengths and weaknesses of the point-particle model. The specific situation considered is the laminar, steady, uniform flow normal to a plane of periodically arranged particles exchanging momentum and heat with the fluid.