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Abstract
In our previous study, we measured the void fraction α, 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 fw and the interfacial friction factor fi based on the annular flow model. The thickness of the falling liquid film δ obtained from the measured α was relatively well expressed by the correlation for the free-falling film, and the obtained fw was well expressed by the Fanning friction factor f for a circular pipe. Measurements of α in vertical pipes under flooding conditions are few. In this study, therefore, we evaluated α and δ 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 δ obtained from the measured dP/dz and the correlation of fw = f were well correlated in terms of the liquid Reynolds number ReL. The obtained δ was well expressed by the Nusselt’s correlation for the free-falling film in the region of laminar flows, but the obtained δ 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 fi.
Nomenclature
| D = | = | diameter (m) |
| D* = | = | dimensionless diameter |
| f = | = | Fanning friction factor |
| fi = | = | interfacial friction factor |
| fw = | = | wall friction factor |
| g = | = | gravitational acceleration (m/s2) |
| h = | = | water level (m) |
| J = | = | superficial velocity (m/s) |
| J* = | = | Wallis parameter |
| K* = | = | Kutateladze parameter |
| L = | = | Laplace capillary length (m) |
| P = | = | pressure (Pa) |
| Re = | = | Reynolds number |
| z = | = | axial coordinate (m) |
| Greek | = | |
| α = | = | void fraction |
| δ = | = | liquid film thickness (m) |
| ν = | = | kinematic viscosity (m2/s) |
| ρ = | = | density (kg/m3) |
| σ = | = | surface tension (N/m) |
Subscript
| G = | = | gas phase |
| i = | = | G or L |
| L = | = | liquid phase or length |
Superscript
| * = | = | dimensionless form |