Water-driven air cavity flow and dispersion in a long partially full circular pipe

Air flow driven by moving water in a long, partially full pipe cavity was investigated experimentally and numerically to provide new insight into recirculating headspace ventilation relevant to sewer gas transport. Air velocity measurements were captured using a smoke concentration pattern-based particle image velocimetry for low-velocity airflow, and air pressure differentials were recorded along the cavity length. The computational fluid dynamics models employed included Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) approaches, treating the water surface as a no-slip moving boundary. The effects of varying headspace height-to-diameter ratios, water surface velocities, and cavity lengths were investigated to characterize air movement, circulation patterns, vertical diffusivity, and longitudinal dispersion. Experimental and numerical data agreed well with RANS and LES for mean longitudinal velocities, offering a computationally efficient alternative and supporting the use of the validated RANS model for efficient parametric analysis. The results revealed a two-layer airflow structure: a lower layer moving with the water direction, occupying roughly one-third of the headspace, and an upper layer moving in the opposite direction. Force balance analysis indicated that the two-layer model underestimated the drag coefficient by approximately 30% compared to the one-layer approach. The normalized relative air velocities of both layers decreased with increasing water surface velocity. The cavity geometry influenced the circulation structure, causing the primary vortex to form closer to the downstream-moving boundary under turbulent conditions. A preliminary analysis based on Taylor dispersion theory suggested that the longitudinal dispersion coefficient can be approximated as the product of headspace height and water surface velocity. Numerical solute-transport simulation followed the analytical solution, with the theoretical estimate slightly overpredicting the dispersion coefficient.