Effects of Active Swimming and Gravitational Settling on Particle Dispersion in Turbulent Pipe Flow

Active swimmers, such as microorganisms, are widespread in natural ecosystems and engineered systems. It is crucial to quantifying the effects of active swimming and gravitational settling during their transport in turbulent flows. Building on the previously established theoretical framework for open-channel flows, this study further addresses the case of circular pipes, a configuration highly common in engineering applications but is much more complicated due to the cylindrical geometry. In this case, active swimming is mainly affected by the flow shear in the radial direction, while gravitational settling acts vertically downward. This difference prevents straightforward superposition of swimmer motions in the same vertical direction as that for open channel flows, making analytical approaches challenging. We first neglect the mechanism of gravitational settling, and adopt the key dimensionless parameter α to quantify the interplay between active swimming and turbulent diffusion. The critical threshold is identified at the same order of magnitude as that for open channel flows, as α~0.1, to distinguish between an active swimming dominated- and turbulence dominated- transport. Numerical simulations using a particle tracking algorithm validate these theoretical results. The influence of gravitational settling is further incorporated by simulations combining particle tracking with Direct Numerical Simulation (DNS), revealing that gravitational settling plays a non-trivial role during transport in turbulent pipe flows, which significantly affects the spatial distribution of the swimmers.