Computational Characterization of Inertial Particle Transport Regimes in Channel Flow

Abstract

Understanding the transport fate of small particles injected from a surface into a crossflow is relevant to applications ranging from debris particulate management in fusion reactors to aerosol dispersion in urban settings. The key question is whether an injected particle remains confined near the wall or penetrates deep into the flow, and how this outcome depends on the particle’s inertia and injection speed. This study develops a computational algorithm that maps transport outcomes across a two-dimensional parameter space defined by the Stokes number St and the normalized injection velocity v0/Uref, producing regime maps that identify the boundaries between near-wall confinement, partial penetration, and midplane crossing. The algorithm was first validated against an exact analytical solution in laminar Poiseuille flow, achieving agreement to within 0.14%. The laminar regime boundaries followed power laws with exponents of −0.81 and −0.85, departing from the analytically predicted exponent of −1 due to coupling between the streamwise and wall-normal particle motion introduced by the velocity profile. The algorithm was then applied to a turbulent carrier flow using eleven frozen snapshots of a DNS channel flow at Reτ = 5200 from the Johns Hopkins Turbulence Database. Within the frozen-field ensemble used here, the turbulent ensemble boundaries have exponents of approximately −0.84 and lower amplitudes than their laminar counterparts, indicating that on average turbulent velocity fluctuations slightly enhance particle penetration beyond what the laminar baseline predicts. The midplane crossing probability transitions sharply near St = 0.179, within the turbophoresis-dominant range. A non-dimensional analysis of secondary forces shows that gravity shifts the regime boundaries by a predictable amount linear in St, confirmed numerically to within 1.13% for St ≤ 0.10, while the Lorentz force on charged particles is negligible for micron-scale grains at typical magnetic field strengths.