Clustering in Euler–Euler and Euler–Lagrange simulations of unbounded homogeneous particle-laden shear

TLDR

Particle‑laden shear flows exhibit strong two‑way coupling even at low volume fractions, and slip between phases induces persistent clustering that modulates the overall flow. In homogeneous shear, clustering arises from preferential concentration of inertial particles forming sheets, whose thickness is set by trajectory crossing and subsequently destabilized by a transverse Rayleigh–Taylor instability driven by shear‑induced rotation, a process examined by comparing Euler–Lagrange simulations with Euler–Euler two‑fluid and anisotropic‑Gaussian models. The two‑fluid Euler–Euler model fails to capture particle‑trajectory crossing, producing discontinuities, whereas the anisotropic‑Gaussian model, based on a kinetic formulation that includes trajectory crossing, eliminates these artifacts.

Abstract

Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle volume fractions, the two-way coupling can be significant due to the large particle to gas density ratio. In this semi-dilute regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concentration of inertial particles in the stretching regions of the flow leads to the formation of highly concentrated particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh–Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler–Lagrange formalism are compared to Euler–Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.