Liquid Film Thickness in Vertical Circular Pipes Under Flooding Conditions at the Top End

In our previous study, we measured the void fraction alpha, pressure gradient dP/dz, and countercurrent flow limitation in a vertical circular pipe (diameter D = 20 mm) under flooding conditions at the square top end and working fluids of air and water to obtain the wall friction factor f(w) and the interfacial friction factor f(i) based on the annular flow model. The thickness of the falling liquid film delta obtained from the measured alpha was relatively well expressed by the correlation for the free-falling film, and the obtained f(w) was well expressed by the Fanning friction factor f for a circular pipe. Measurements of alpha in vertical pipes under flooding conditions are few. In this study, therefore, we evaluated alpha and delta from the measured dP/dz under flooding at the square top end reported by Bharathan et al. with D = 50.8 mm and air-water and by Ilyukhin et al. with D = 20 mm and working fluids of steam and water at pressures of P = 0.6 to 4.1 MPa. As a result, we found that delta obtained from the measured dP/dz and the correlation of f(w) = f were well correlated in terms of the liquid Reynolds number Re-L. The obtained delta was well expressed by the Nusselt's correlation for the free-falling film in the region of laminar flows, but the obtained delta was larger than the Feind's correlation for the free-falling film in the region of turbulent flows due to the interfacial friction. We also discussed effects of the diameter and fluid properties on the interfacial friction factor f(i).