Effect of Lagrangian time scales on the statistical simulations of droplet penetration through turbulent pipe flows

Penetration of droplets in fully-developed turbulent pipe flows (vertical configuration) was studied numerically. Two Reynolds numbers ($R{e}_D$ = 37,700 and 11,700) based on the pipe diameter were used in the simulations. Statistics used in the single-phase flow characterization (mean velocities, root mean square fluctuation velocities, and turbulence dissipation rate) were obtained from the law of the wall relationships in addition to curve-fitting from direct numerical simulation (DNS) data found in the literature. The droplet phase was simulated using a one-way coupling Lagrangian random-walk eddy interaction model (EIM). Monodispersed droplets, ranging from 1.78 to $26.83\mu m$, were released separately in the pipe-flow computational domain. A modified eddy lifetime, based on local turbulent Reynolds numbers ($R{e}_{{\lambda }_T}$) and velocity fluctuations perpendicular to the walls, is proposed. Simulation results of droplet penetration show relatively good agreement against experimental data obtained from the literature.