Quantification of Inertial Particle Clustering and Geometric Confinement Effects in Turbulent Flow Through a Porous Cell*

Quantifying how turbulence affects inertial particle clustering, migration,  and deposition within confined geometries of porous beds is of importance in several applications such as hyporheic exchange of river beds, gravel packs in enhanced oil recovery, among others. Direct numerical simulation is performed to investigate effect of turbulent flow in a face centered cubic porous unit cell on the transport of inertial particles at different Stokes numbers (0.01, 0.1, 0.5, 1, and 2) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and collision of particles with pore walls is modeled as perfectly elastic specular reflection. Statistics on Voronoi tessellation volume and its divergence are used to quantify clustering, void formation, and effect of geometric confinement. The general features of cluster and void formation are similar to those in forced, isotropic turbulence, but some very fine scale clusters are developed owing to collisions with wall. Multiscale wavelet analysis also shows signature of the confined geometry on the scale dependent energy spectra of number density.